Question 1

Simplify the expression algebraically. 
 8sin⁡(π2+x) 8 \sin \left( \frac { \pi } { 2 } + x \right) 8sin(2π​+x)

Accepted Answer

A)    −8cos⁡x- 8 \cos x−8cosx 
B)    18cos⁡x\frac { 1 } { 8 } \cos x81​cosx 
C)    8cos⁡x8 \cos x8cosx 
D)    8sin⁡x8 \sin x8sinx 
E)    −18cos⁡x- \frac { 1 } { 8 } \cos x−81​cosx

Question 2

The monthly sales S (in hundreds of units)  of baseball equipment for an Internet sporting goods site are approximated by  S=60.5−48.5cos⁡πt6S = 60.5 - 48.5 \cos \frac { \pi t } { 6 }S=60.5−48.5cos6πt​ 
where  ttt  is the time (in months) , with  t=1t = 1t=1  corresponding to January. Determine the months when sales exceed 7700 units at any time during the month.

Accepted Answer

A)   March through September
B)   April through August
C)   March through August
D)   August through April
E)   May through September

Question 3

Use the given values to evaluate (if possible)  three trigonometric functions cosx, cscx, tanx. 
 sin⁡x=15\sin x = \frac { 1 } { 5 }sinx=51​

Accepted Answer

A)   cos⁡x=265csc⁡x=15\begin{array} { l } \cos x = \frac { 2 \sqrt { 6 } } { 5 } \\csc x = \frac { 1 } { 5 }\end{array}cosx=526c-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'/>​​cscx=51​​  tan⁡x=612	an x = \frac { \sqrt { 6 } } { 12 }tanx=126c-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)   cos⁡x=−265csc⁡x=−5tan⁡x=−612\begin{array} { l } \cos x = - \frac { 2 \sqrt { 6 } } { 5 } \\csc x = - 5 \	an x = - \frac { \sqrt { 6 } } { 12 }\end{array}cosx=−526c-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'/>​​cscx=−5tanx=−126c-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)   cos⁡x=265\cos x = \frac { 2 \sqrt { 6 } } { 5 }cosx=526c-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'/>​​   csc⁡x=5\csc x = 5cscx=5   tan⁡x=−612	an x = - \frac { \sqrt { 6 } } { 12 }tanx=−126c-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)   cos⁡x=265csc⁡x=5tan⁡x=612\begin{array} { l } \cos x = \frac { 2 \sqrt { 6 } } { 5 } \\csc x = 5 \	an x = \frac { \sqrt { 6 } } { 12 }\end{array}cosx=526c-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'/>​​cscx=5tanx=126c-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'/>​​​ 
E)   cos⁡x=−265csc⁡x=5tan⁡x=612\begin{array} { l } \cos x = - \frac { 2 \sqrt { 6 } } { 5 } \\csc x = 5 \	an x = \frac { \sqrt { 6 } } { 12 }\end{array}cosx=−526c-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'/>​​cscx=5tanx=126c-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

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places.  a=1,b=12,c=23a = 1 , b = \frac { 1 } { 2 } , c = \frac { 2 } { 3 }a=1,b=21​,c=32​

Accepted Answer

A)    0.710.710.71 
B)    0.740.740.74 
C)    0.580.580.58 
D)    2.52.52.5 
E)    0.150.150.15

Question 5

Find the area of the triangle having the indicated angle and sides. 
 A=5∘19′,b=4.7,c=22A = 5 ^ { \circ } 19 ^ { \prime } , b = 4.7 , c = 22A=5∘19′,b=4.7,c=22  (Round your answer to one decimal place.)

Accepted Answer

A)    4.84.84.8 
B)    3.83.83.8 
C)    5.85.85.8 
D)    6.86.86.8 
E)    9.69.69.6

Question 6

Evaluate the following expression. 
 7tan⁡(π2−θ) tan⁡θ7 	an \left( \frac { \pi } { 2 } - 	heta ight)  	an 	heta7tan(2π​−θ) tanθ

Accepted Answer

A)   6
B)   7
C)    −8- 8−8 
D)    −7- 7−7 
E)   8

Question 7

Find all solutions of the given equation in the interval  [0,2π) [ 0,2 \pi ) [0,2π)   
 cos⁡x2−sin⁡x=0\cos \frac { x } { 2 } - \sin x = 0cos2x​−sinx=0

Accepted Answer

A)    x=π3,5π3x = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }x=3π​,35π​ 
B)    x=π,5π3x = \pi , \frac { 5 \pi } { 3 }x=π,35π​ 
C)    x=π3,π,5π3x = \frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }x=3π​,π,35π​ 
D)    x=π3,πx = \frac { \pi } { 3 } , \pix=3π​,π 
E)    x=πx = \pix=π

Exam 5: Analytic Trigonometry

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. $\sin x = \frac { 1 } { 5 }$

Correct Answer
verified

Correct Answer
verified

Find all solutions of the given equation in the interval $[ 0,2 \pi )$ $\cos \frac { x } { 2 } - \sin x = 0$

Correct Answer
verified

Evaluate the following expression. $7 \tan \left( \frac { \pi } { 2 } - \theta \right) \tan \theta$

Correct Answer
verified

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places. $a = 1 , b = \frac { 1 } { 2 } , c = \frac { 2 } { 3 }$

Correct Answer
verified

Find the area of the triangle having the indicated angle and sides. $A = 5 ^ { \circ } 19 ^ { \prime } , b = 4.7 , c = 22$ (Round your answer to one decimal place.)

Correct Answer
verified

Simplify the expression algebraically. $8 \sin \left( \frac { \pi } { 2 } + x \right)$

Correct Answer
verified

Exam 5: Analytic Trigonometry

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. sin⁡x=15\sin x = \frac { 1 } { 5 }sinx=51​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find all solutions of the given equation in the interval [0,2π) [ 0,2 \pi ) [0,2π) cos⁡x2−sin⁡x=0\cos \frac { x } { 2 } - \sin x = 0cos2x​−sinx=0

Correct AnswerverifiedShow Answer

Evaluate the following expression. 7tan⁡(π2−θ) tan⁡θ7 \tan \left( \frac { \pi } { 2 } - \theta \right) \tan \theta7tan(2π​−θ) tanθ

Correct AnswerverifiedShow Answer

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places. a=1,b=12,c=23a = 1 , b = \frac { 1 } { 2 } , c = \frac { 2 } { 3 }a=1,b=21​,c=32​

Correct AnswerverifiedShow Answer

Find the area of the triangle having the indicated angle and sides. A=5∘19′,b=4.7,c=22A = 5 ^ { \circ } 19 ^ { \prime } , b = 4.7 , c = 22A=5∘19′,b=4.7,c=22 (Round your answer to one decimal place.)

Correct AnswerverifiedShow Answer

Simplify the expression algebraically. 8sin⁡(π2+x) 8 \sin \left( \frac { \pi } { 2 } + x \right) 8sin(2π​+x)

Correct AnswerverifiedShow Answer

Use the given values to evaluate (if possible) three trigonometric functions cosx, cscx, tanx. $\sin x = \frac { 1 } { 5 }$

Correct Answer
verified

Correct Answer
verified

Find all solutions of the given equation in the interval $[ 0,2 \pi )$ $\cos \frac { x } { 2 } - \sin x = 0$

Correct Answer
verified

Evaluate the following expression. $7 \tan \left( \frac { \pi } { 2 } - \theta \right) \tan \theta$

Correct Answer
verified

Use the Heron's formula to find the area of the triangle. Round your answer upto two decimal places. $a = 1 , b = \frac { 1 } { 2 } , c = \frac { 2 } { 3 }$

Correct Answer
verified

Find the area of the triangle having the indicated angle and sides. $A = 5 ^ { \circ } 19 ^ { \prime } , b = 4.7 , c = 22$ (Round your answer to one decimal place.)

Correct Answer
verified

Simplify the expression algebraically. $8 \sin \left( \frac { \pi } { 2 } + x \right)$

Correct Answer
verified