Question 1

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
- A=53.7∘,C=41.7\mathrm { A } = 53.7 ^ { \circ } , \mathrm { C } = 41.7A=53.7∘,C=41.7

Accepted Answer

A)    B=36.3∘,a=33.6, b=24.7\mathrm { B } = 36.3 ^ { \circ } , \mathrm { a } = 33.6 , \mathrm {~b} = 24.7B=36.3∘,a=33.6, b=24.7 
B)    B=36.3∘,a=24.7, b=33.6\mathrm { B } = 36.3 ^ { \circ } , \mathrm { a } = 24.7 , \mathrm {~b} = 33.6B=36.3∘,a=24.7, b=33.6 
C)    B=53.7∘,a=33.6, b=24.7\mathrm { B } = 53.7 ^ { \circ } , \mathrm { a } = 33.6 , \mathrm {~b} = 24.7B=53.7∘,a=33.6, b=24.7 
D)    B=53.7∘,a=24.7, b=33.6\mathrm { B } = 53.7 ^ { \circ } , \mathrm { a } = 24.7 , \mathrm {~b} = 33.6B=53.7∘,a=24.7, b=33.6

Question 2

Use a calculator to find the value of the expression rounded to two decimal places.
- sin⁡−1(33) \sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right) sin−1(33​​)

Accepted Answer

A)    0.620.620.62 
B)    35.2635.2635.26 
C)    0.960.960.96 
D)    54.7454.7454.74

Question 3

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function
of the given angle. Give an exact answer with a rational denominator.
-Find  cot⁡θ\cot 	hetacotθ .

Accepted Answer

A)    25\frac { 2 } { 5 }52​ 
B)    22929\frac { 2 \sqrt { 29 } } { 29 }29229c-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)    52\frac { 5 } { 2 }25​ 
D)    52929\frac { 5 \sqrt { 29 } } { 29 }29529c-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 4

Determine the amplitude or period as requested.
-Period of  y=−14sin⁡xy = - \frac { 1 } { 4 } \sin xy=−41​sinx

Accepted Answer

A)    2π2 \pi2π 
B)    π\piπ 
C)    π4\frac { \pi } { 4 }4π​ 
D)    −14- \frac { 1 } { 4 }−41​

Question 5

Additional Concepts
- y=sec⁡(2x+π4) +1y=\sec \left(2 x+\frac{\pi}{4}\right) +1y=sec(2x+4π​) +1

Accepted Answer

A)  
B)  
C)  
D)

Question 6

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
-A radio transmission tower is 230 feet tall. How long should a guy wire be if it is to be attached 9 feet from the top and is to make an angle of 35°  35∘35 ^ { \circ }35∘  with the ground? Give your answer to the nearest tenth of a foot.

Accepted Answer

A)   385.3 feet
B)   401.0 feet
C)   269.8 feet
D)   280.8 feet

Question 7

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
-The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 35 minutes? If necessary, round the answer to two decimal places.

Accepted Answer

A)    14.6614.6614.66  inches
B)    17.1717.1717.17  inches
C)    15.8915.8915.89  inches
D)    12.9212.9212.92  inches

Question 8

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function
of the given angle. Give an exact answer with a rational denominator.
-Find  cos⁡θ\cos 	hetacosθ

Accepted Answer

A)    33434\frac { 3 \sqrt { 34 } } { 34 }34334c-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)    345\frac { \sqrt { 34 } } { 5 }534c-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)    343\frac { \sqrt { 34 } } { 3 }334c-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)    53434\frac { 5 \sqrt { 34 } } { 34 }34534c-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 9

Find the exact value of the expression. Do not use a calculator.
-If  tan⁡θ=2	an 	heta = 2tanθ=2 , find the exact value of  cot⁡(π2−θ) \cot \left( \frac { \pi } { 2 } - 	heta ight) cot(2π​−θ)  .

Accepted Answer

A)   2
B)    12\frac { 1 } { 2 }21​ 
C)   1
D)   3

Question 10

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
- r=45\mathrm { r } = 45r=45  inches,  θ=35∘	heta = 35 ^ { \circ }θ=35∘

Accepted Answer

A)    27.4927.4927.49  inches
B)    29.9229.9229.92  inches
C)    28.7828.7828.78  inches
D)    25.6425.6425.64  inches

Question 11

Graph the function.
- f(x) =4sin⁡x,g(x) =sin⁡2x;h(x) =(f+g) (x) f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x) f(x) =4sinx,g(x) =sin2x;h(x) =(f+g) (x)

Accepted Answer

A)  
B)  
C)  
D)

Question 12

Graph Variations of y = csc x and y = sec x
- y=csc⁡xy=\csc xy=cscx

Accepted Answer

A)  
B)  
C)  
D)

Question 13

Use reference angles to find the exact value of the expression. Do not use a calculator.
- csc⁡−2π3\csc \frac { - 2 \pi } { 3 }csc3−2π​

Accepted Answer

A)    −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'/>​​ 
B)    −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'/>​ 
C)    −3- \sqrt { 3 }−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'/>​ 
D)    −12- \frac { 1 } { 2 }−21​

Question 14

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
-A building 150 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree) ? (Assume the person's eyes are 5 feet above ground level.)

Accepted Answer

A)    55.41∘55.41 ^ { \circ }55.41∘ 
B)    56.31∘56.31 ^ { \circ }56.31∘ 
C)    46.40∘46.40 ^ { \circ }46.40∘ 
D)    43.60∘43.60 ^ { \circ }43.60∘

Question 15

Use reference angles to find the exact value of the expression. Do not use a calculator.
- sec⁡5π4\sec \frac { 5 \pi } { 4 }sec45π​

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)    −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'/>​​ 
C)   -2
D)    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'/>​​  )

Question 16

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
- sec⁡250∘−tan⁡250∘\sec ^ { 2 } 50 ^ { \circ } - 	an ^ { 2 } 50 ^ { \circ }sec250∘−tan250∘

Accepted Answer

A)   1
B)   0
C)    0.500.500.50 
D)    0.250.250.25

Question 17

Graph Variations of y = cot x
- y=4cot⁡π2xy = 4 \cot \frac { \pi } { 2 } xy=4cot2π​x

Accepted Answer

A)  
B)  
C)  
D)

Question 18

Understand the Graphs of y = csc x and y = sec x
Use the graph to obtain the graph of the reciprocal function. Give the equation of the function for the graph that
you obtain.
- y=2cos⁡3πxy=2 \cos 3 \pi xy=2cos3πx

Accepted Answer

A)   y=2sec⁡3πxy=2 \sec 3 \pi xy=2sec3πx 
B)    y=2sin⁡3πxy = 2 \sin 3 \pi xy=2sin3πx 
C)    y=2csc⁡3πxy = 2 \csc 3 \pi xy=2csc3πx 
D)    y=2cot⁡3πxy = 2 \cot 3 \pi xy=2cot3πx

Question 19

Find the reference angle for the given angle.
- 27∘27 ^ { \circ }27∘

Accepted Answer

A)    27∘27 ^ { \circ }27∘ 
B)    63∘63 ^ { \circ }63∘ 
C)    153∘153 ^ { \circ }153∘ 
D)    117∘117 ^ { \circ }117∘

Question 20

Determine the amplitude or period as requested.
Graph Variations of y = cos x
-Amplitude of  y=34cos⁡(−6π5x) y = \frac { 3 } { 4 } \cos \left( - \frac { 6 \pi } { 5 } x \right) y=43​cos(−56π​x)

Accepted Answer

A)    34\frac { 3 } { 4 }43​ 
B)    53\frac { 5 } { 3 }35​ 
C)    4π3\frac { 4 \pi } { 3 }34π​ 
D)    6π5\frac { 6 \pi } { 5 }56π​

Exam 5: Trigonometric Functions

Find the exact value of the expression. Do not use a calculator. -If $\tan \theta = 2$ , find the exact value of $\cot \left( \frac { \pi } { 2 } - \theta \right)$ .

Correct Answer
verified

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places. -The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 35 minutes? If necessary, round the answer to two decimal places.

Correct Answer
verified

Correct Answer
verified

Use a calculator to find the value of the expression rounded to two decimal places. - $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right)$

Correct Answer
verified

Correct Answer
verified

Determine the amplitude or period as requested. Graph Variations of y = cos x -Amplitude of $y = \frac { 3 } { 4 } \cos \left( - \frac { 6 \pi } { 5 } x \right)$

Correct Answer
verified

Use reference angles to find the exact value of the expression. Do not use a calculator. - $\sec \frac { 5 \pi } { 4 }$

Correct Answer
verified

Graph Variations of y = csc x and y = sec x - $y=\csc x$ $Graph Variations of y = csc x and y = sec x - y=\csc x A) B) C) D)$

Correct Answer
verified

Determine the amplitude or period as requested. -Period of $y = - \frac { 1 } { 4 } \sin x$

Correct Answer
verified

Additional Concepts - $y=\sec \left(2 x+\frac{\pi}{4}\right) +1$ $Additional Concepts - y=\sec \left(2 x+\frac{\pi}{4}\right) +1 A) B) C) D)$

Correct Answer
verified

Use reference angles to find the exact value of the expression. Do not use a calculator. - $\csc \frac { - 2 \pi } { 3 }$

Correct Answer
verified

Correct Answer
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Correct Answer
verified

Graph the function. - $f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x)$ $Graph the function. - f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x) A) B) C) D)$

Correct Answer
verified

θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. - $\sec ^ { 2 } 50 ^ { \circ } - \tan ^ { 2 } 50 ^ { \circ }$

Correct Answer
verified

Graph Variations of y = cot x - $y = 4 \cot \frac { \pi } { 2 } x$ $Graph Variations of y = cot x - y = 4 \cot \frac { \pi } { 2 } x A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places. - $\mathrm { r } = 45$ inches, $\theta = 35 ^ { \circ }$

Correct Answer
verified

Find the reference angle for the given angle. - $27 ^ { \circ }$

Correct Answer
verified

Correct Answer
verified

Exam 5: Trigonometric Functions

Find the exact value of the expression. Do not use a calculator. -If tan⁡θ=2\tan \theta = 2tanθ=2 , find the exact value of cot⁡(π2−θ) \cot \left( \frac { \pi } { 2 } - \theta \right) cot(2π​−θ) .

Correct AnswerverifiedShow Answer

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places. -The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 35 minutes? If necessary, round the answer to two decimal places.

Correct AnswerverifiedShow Answer

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. -Find cos⁡θ\cos \thetacosθ

Correct AnswerverifiedShow Answer

Use a calculator to find the value of the expression rounded to two decimal places. - sin⁡−1(33) \sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right) sin−1(33​​)

Correct AnswerverifiedShow Answer

Understand the Graphs of y = csc x and y = sec x Use the graph to obtain the graph of the reciprocal function. Give the equation of the function for the graph that you obtain. - y=2cos⁡3πxy=2 \cos 3 \pi xy=2cos3πx

Correct AnswerverifiedShow Answer

Determine the amplitude or period as requested. Graph Variations of y = cos x -Amplitude of y=34cos⁡(−6π5x) y = \frac { 3 } { 4 } \cos \left( - \frac { 6 \pi } { 5 } x \right) y=43​cos(−56π​x)

Correct AnswerverifiedShow Answer

Use reference angles to find the exact value of the expression. Do not use a calculator. - sec⁡5π4\sec \frac { 5 \pi } { 4 }sec45π​

Correct AnswerverifiedShow Answer

Graph Variations of y = csc x and y = sec x - y=csc⁡xy=\csc xy=cscx

Correct AnswerverifiedShow Answer

Determine the amplitude or period as requested. -Period of y=−14sin⁡xy = - \frac { 1 } { 4 } \sin xy=−41​sinx

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Additional Concepts - y=sec⁡(2x+π4) +1y=\sec \left(2 x+\frac{\pi}{4}\right) +1y=sec(2x+4π​) +1

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Use reference angles to find the exact value of the expression. Do not use a calculator. - csc⁡−2π3\csc \frac { - 2 \pi } { 3 }csc3−2π​

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Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest tenth of a degree. - A=53.7∘,C=41.7\mathrm { A } = 53.7 ^ { \circ } , \mathrm { C } = 41.7A=53.7∘,C=41.7

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Graph the function. - f(x) =4sin⁡x,g(x) =sin⁡2x;h(x) =(f+g) (x) f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x) f(x) =4sinx,g(x) =sin2x;h(x) =(f+g) (x)

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θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. - sec⁡250∘−tan⁡250∘\sec ^ { 2 } 50 ^ { \circ } - \tan ^ { 2 } 50 ^ { \circ }sec250∘−tan250∘

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Graph Variations of y = cot x - y=4cot⁡π2xy = 4 \cot \frac { \pi } { 2 } xy=4cot2π​x

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Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. -Find cot⁡θ\cot \thetacotθ .

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Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places. - r=45\mathrm { r } = 45r=45 inches, θ=35∘\theta = 35 ^ { \circ }θ=35∘

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Find the reference angle for the given angle. - 27∘27 ^ { \circ }27∘

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Find the exact value of the expression. Do not use a calculator. -If $\tan \theta = 2$ , find the exact value of $\cot \left( \frac { \pi } { 2 } - \theta \right)$ .

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Use a calculator to find the value of the expression rounded to two decimal places. - $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right)$

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Determine the amplitude or period as requested. Graph Variations of y = cos x -Amplitude of $y = \frac { 3 } { 4 } \cos \left( - \frac { 6 \pi } { 5 } x \right)$

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Use reference angles to find the exact value of the expression. Do not use a calculator. - $\sec \frac { 5 \pi } { 4 }$

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Graph Variations of y = csc x and y = sec x - $y=\csc x$ $Graph Variations of y = csc x and y = sec x - y=\csc x A) B) C) D)$

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Determine the amplitude or period as requested. -Period of $y = - \frac { 1 } { 4 } \sin x$

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Additional Concepts - $y=\sec \left(2 x+\frac{\pi}{4}\right) +1$ $Additional Concepts - y=\sec \left(2 x+\frac{\pi}{4}\right) +1 A) B) C) D)$

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Use reference angles to find the exact value of the expression. Do not use a calculator. - $\csc \frac { - 2 \pi } { 3 }$

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Graph the function. - $f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x)$ $Graph the function. - f(x) =4 \sin x, g(x) =\sin 2 x ; h(x) =(f+g) (x) A) B) C) D)$

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θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. - $\sec ^ { 2 } 50 ^ { \circ } - \tan ^ { 2 } 50 ^ { \circ }$

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Graph Variations of y = cot x - $y = 4 \cot \frac { \pi } { 2 } x$ $Graph Variations of y = cot x - y = 4 \cot \frac { \pi } { 2 } x A) B) C) D)$

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Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places. - $\mathrm { r } = 45$ inches, $\theta = 35 ^ { \circ }$

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Find the reference angle for the given angle. - $27 ^ { \circ }$

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