Question 1

Without using a calculator, give the exact trigonometric function value with rational denominator.
-sec 45

Accepted Answer

A)    2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)   1
C)    12\frac { 1 } { 2 }21​ 
D)    233\frac { 2 \sqrt { 3 } } { 3 }323c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​  °

Question 2

Solve the right triangle.
-a = 3.6 m, B = 30.3°, C = 90° Round values to one decimal place.

Accepted Answer

A)  A = 59.7°, b = 4.4 m, c = 5.7 m
B)  A = 59.7°, b = 2.1 m, c = 4.2 m
C)  A = 59.7°, b = 1 m, c = 3.7 m
D)  A = 59.7°, b = 4.4 m, c = 4.2 m

Question 3

Evaluate.
- 3cot⁡245∘+tan⁡4300∘−5sin⁡40∘3 \cot ^ { 2 } 45 ^ { \circ } + 	an ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }3cot245∘+tan4300∘−5sin40∘

Accepted Answer

A)   7
B)   12
C)   84
D)   14

Question 4

Solve the problem.
-Find the exact value of x in the figure.

Accepted Answer

A)    23323 \sqrt { 3 }233c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    22622 \sqrt { 6 }226c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    22322 \sqrt { 3 }223c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    20320 \sqrt { 3 }203c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 5

Find the exact value of the expression.
-cos 210°

Accepted Answer

A)    −32- \frac { \sqrt { 3 } } { 2 }−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    22\frac { \sqrt { 2 } } { 2 }22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    −22- \frac { \sqrt { 2 } } { 2 }−22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    32\frac { \sqrt { 3 } } { 2 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​

Question 6

Find the exact value of the expression.
-sec (-1215°)

Accepted Answer

A)    −1- 1−1 
B)    22\frac { \sqrt { 2 } } { 2 }22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    −33- \frac { \sqrt { 3 } } { 3 }−33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    −2- \sqrt { 2 }−2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 7

Find a solution for the equation. Assume that all angles are acute angles.
-sec ϴ = csc(ϴ + 46°)

Accepted Answer

A)  23°
B)  67°
C)  22°
D)  68°

Question 8

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-cos 47° cos 133° - sin 47° sin 133°

Accepted Answer

A)  2
B)  0
C)  1
D)  -1

Question 9

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-tan ϴ = 1.5047547

Accepted Answer

A)  56.3935717°
B)  123.606428°
C)  33.6064283°
D)  236.393572°

Question 10

Use a calculator to decide whether the statement is true or false.
-cos (2 ·30°)= 2 · cos 30°

Accepted Answer

A) True 
 B)False

Question 11

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-sin 77°

Accepted Answer

A)  csc 13°
B)  sin 167°
C)  cos 13°
D)  cos 77°

Question 12

Solve the problem.
-An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer) ?

Accepted Answer

A)  4736 km
B)  492 km
C)  4710 km
D)  52 km

Question 13

Solve the problem.
-The index of refraction for air, Ia, is 1.0003. The index of refraction for water, Iw, is 1.3. If  IWIa=sin⁡Asin⁡W\frac { \mathrm { I } _ { \mathrm { W } } } { \mathrm { I } _ { \mathrm { a } } } = \frac { \sin \mathrm { A } } { \sin \mathrm { W } }Ia​IW​​=sinWsinA​ , and  A=31.5∘\mathrm { A } = 31.5 ^ { \circ }A=31.5∘ , find  W\mathrm { W }W  to the nearest tenth.

Accepted Answer

A)    22.7∘22.7 ^ { \circ }22.7∘ 
B)    23.7∘23.7 ^ { \circ }23.7∘ 
C)    21.7∘21.7 ^ { \circ }21.7∘ 
D)    20.7∘20.7 ^ { \circ }20.7∘

Question 14

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find  sec⁡B\sec BsecB  when  a=2a = 2a=2  and  b=9b = 9b=9 .

Accepted Answer

A)    28585\frac { 2 \sqrt { 85 } } { 85 }85285c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    98585\frac { 9 \sqrt { 85 } } { 85 }85985c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    852\frac { \sqrt { 85 } } { 2 }285c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    2859\frac { 2 \sqrt { 85 } } { 9 }9285c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​

Question 15

Solve the problem.
-The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ, where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0
For downhill travel) . What is the grade resistance (to the nearest pound) of a 2100-lb car traveling
Downhill on a 5° grade (ϴ = -5°) ?

Accepted Answer

A)  183 lb
B)  -2105 lb
C)  2105 lb
D)  -183 lb

Question 16

Solve the problem.
-Find a formula for the area of the figure in terms of s.

Accepted Answer

A)    36 s2\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }63c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ s2 
B)    6 s2\sqrt { 6 } \mathrm {~s} ^ { 2 }6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ s2 
C)    64s2\frac { \sqrt { 6 } } { 4 } s ^ { 2 }46c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​s2 
D)    32 s2\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ s2

Question 17

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-
 a=50.26ft,c=231ft\mathrm { a } = 50.26 \mathrm { ft } , \mathrm { c } = 231 \mathrm { ft }a=50.26ft,c=231ft 
Round the missing side length to two decimal places.

Accepted Answer

A)    A=13∘34′,B=76∘26′,b=225.47ft\mathrm { A } = 13 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 76 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 225.47 \mathrm { ft }A=13∘34′,B=76∘26′,b=225.47ft 
B)    A=10∘34′,B=79∘26′,b=236.74ftA = 10 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 79 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 236.74 \mathrm { ft }A=10∘34′,B=79∘26′,b=236.74ft 
C)    A=12∘34′,B=77∘26′,b=209.69ft\mathrm { A } = 12 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 77 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 209.69 \mathrm { ft }A=12∘34′,B=77∘26′,b=209.69ft 
D)    A=12∘34′;B=77∘26′;b=225.47ftA = 12 ^ { \circ } 34 ^ { \prime } ; B = 77 ^ { \circ } 26 ^ { \prime } ; b = 225.47 \mathrm { ft }A=12∘34′;B=77∘26′;b=225.47ft

Question 18

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant  III  and the positive  xxx -axis is  22\frac { \sqrt { 2 } } { 2 }22​​ .

Accepted Answer

A)    y=3xy = \sqrt { 3 } xy=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​x 
B)    y=22xy = \frac { \sqrt { 2 } } { 2 } xy=22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​x 
C)    y=33xy = \frac { \sqrt { 3 } } { 3 } xy=33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​x 
D)    y=xy = xy=x

Question 19

Find a solution for the equation. Assume that all angles are acute angles.
- sec⁡(θ+12∘) =csc⁡(2θ+15∘) \sec \left( 	heta + 12 ^ { \circ } ight)  = \csc \left( 2 	heta + 15 ^ { \circ } ight) sec(θ+12∘) =csc(2θ+15∘)

Accepted Answer

A)    23.5∘23.5 ^ { \circ }23.5∘ 
B)    19∘19 ^ { \circ }19∘ 
C)    15∘15 ^ { \circ }15∘ 
D)    21∘21 ^ { \circ }21∘

Question 20

Solve the problem for the given information.
-What angle does the line y = x make with the positive x-axis?

Accepted Answer

A)  90°
B)  60°
C)  30°
D)  45°

Exam 2: Acute Angles and Right Triangles

Correct Answer
verified

Use a calculator to decide whether the statement is true or false. -cos (2 ·30°)= 2 · cos 30°

Correct Answer
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Find a solution for the equation. Assume that all angles are acute angles. - $\sec \left( \theta + 12 ^ { \circ } \right) = \csc \left( 2 \theta + 15 ^ { \circ } \right)$

Correct Answer
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Correct Answer
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Correct Answer
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Solve the right triangle. -a = 3.6 m, B = 30.3°, C = 90° Round values to one decimal place.

Correct Answer
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Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -tan ϴ = 1.5047547

Correct Answer
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Evaluate. - $3 \cot ^ { 2 } 45 ^ { \circ } + \tan ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }$

Correct Answer
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Solve the problem. -An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer) ?

Correct Answer
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Solve the problem for the given information. -What angle does the line y = x make with the positive x-axis?

Correct Answer
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Find the exact value of the expression. -cos 210°

Correct Answer
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Correct Answer
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Correct Answer
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Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 2 } } { 2 }$ .

Correct Answer
verified

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -sin 77°

Correct Answer
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Without using a calculator, give the exact trigonometric function value with rational denominator. -sec 45

Correct Answer
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Solve the problem. -Find the exact value of x in the figure. $Solve the problem. -Find the exact value of x in the figure. A) 23 \sqrt { 3 } B) 22 \sqrt { 6 } C) 22 \sqrt { 3 } D) 20 \sqrt { 3 }$

Correct Answer
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Find the exact value of the expression. -sec (-1215°)

Correct Answer
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Find a solution for the equation. Assume that all angles are acute angles. -sec ϴ = csc(ϴ + 46°)

Correct Answer
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Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 47° cos 133° - sin 47° sin 133°

Correct Answer
verified

Exam 2: Acute Angles and Right Triangles

Correct AnswerverifiedShow Answer

Use a calculator to decide whether the statement is true or false. -cos (2 ·30°)= 2 · cos 30°

Correct AnswerverifiedShow Answer

Find a solution for the equation. Assume that all angles are acute angles. - sec⁡(θ+12∘) =csc⁡(2θ+15∘) \sec \left( \theta + 12 ^ { \circ } \right) = \csc \left( 2 \theta + 15 ^ { \circ } \right) sec(θ+12∘) =csc(2θ+15∘)

Correct AnswerverifiedShow Answer

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - a=50.26ft,c=231ft\mathrm { a } = 50.26 \mathrm { ft } , \mathrm { c } = 231 \mathrm { ft }a=50.26ft,c=231ft Round the missing side length to two decimal places.

Correct AnswerverifiedShow Answer

Solve the problem. -Find a formula for the area of the figure in terms of s.

Correct AnswerverifiedShow Answer

Solve the right triangle. -a = 3.6 m, B = 30.3°, C = 90° Round values to one decimal place.

Correct AnswerverifiedShow Answer

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -tan ϴ = 1.5047547

Correct AnswerverifiedShow Answer

Evaluate. - 3cot⁡245∘+tan⁡4300∘−5sin⁡40∘3 \cot ^ { 2 } 45 ^ { \circ } + \tan ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }3cot245∘+tan4300∘−5sin40∘

Correct AnswerverifiedShow Answer

Solve the problem. -An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer) ?

Correct AnswerverifiedShow Answer

Solve the problem for the given information. -What angle does the line y = x make with the positive x-axis?

Correct AnswerverifiedShow Answer

Find the exact value of the expression. -cos 210°

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant III and the positive xxx -axis is 22\frac { \sqrt { 2 } } { 2 }22​​ .

Correct AnswerverifiedShow Answer

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -sin 77°

Correct AnswerverifiedShow Answer

Without using a calculator, give the exact trigonometric function value with rational denominator. -sec 45

Correct AnswerverifiedShow Answer

Solve the problem. -Find the exact value of x in the figure.

Correct AnswerverifiedShow Answer

Find the exact value of the expression. -sec (-1215°)

Correct AnswerverifiedShow Answer

Find a solution for the equation. Assume that all angles are acute angles. -sec ϴ = csc(ϴ + 46°)

Correct AnswerverifiedShow Answer

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 47° cos 133° - sin 47° sin 133°

Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
verified

Find a solution for the equation. Assume that all angles are acute angles. - $\sec \left( \theta + 12 ^ { \circ } \right) = \csc \left( 2 \theta + 15 ^ { \circ } \right)$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Evaluate. - $3 \cot ^ { 2 } 45 ^ { \circ } + \tan ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 2 } } { 2 }$ .

Correct Answer
verified

Correct Answer
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Correct Answer
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Solve the problem. -Find the exact value of x in the figure. $Solve the problem. -Find the exact value of x in the figure. A) 23 \sqrt { 3 } B) 22 \sqrt { 6 } C) 22 \sqrt { 3 } D) 20 \sqrt { 3 }$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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