Question 1

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

Accepted Answer

A)  $0.71$ 
B)  $0.74$ 
C)  $0.58$ 
D)  $2.5$ 
E)  $0.15$ 
A)  $0.71$ 
B)  $0.74$ 
C)  $0.58$ 
D)  $2.5$ 
E)  $0.15$

Question 2

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.)

Accepted Answer

A)  $4.8$ 
B)  $3.8$ 
C)  $5.8$ 
D)  $6.8$ 
E)  $9.6$ 
A)  $4.8$ 
B)  $3.8$ 
C)  $5.8$ 
D)  $6.8$ 
E)  $9.6$

Question 3

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by $S = 60.5 - 48.5 \cos \frac { \pi t } { 6 }$
where $t$ is the time (in months), with $t = 1$ 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 
A)  March through September 
B)  April through August 
C)  March through August 
D)  August through April 
E)  May through September

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $x = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
B)  $x = \pi , \frac { 5 \pi } { 3 }$ 
C)  $x = \frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }$ 
D)  $x = \frac { \pi } { 3 } , \pi$ 
E)  $x = \pi$ 
A)  $x = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
B)  $x = \pi , \frac { 5 \pi } { 3 }$ 
C)  $x = \frac { \pi } { 3 } , \pi , \frac { 5 \pi } { 3 }$ 
D)  $x = \frac { \pi } { 3 } , \pi$ 
E)  $x = \pi$

Question 6

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

Accepted Answer

A) 
$\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = \frac { 1 } { 5 }
\end{array}$
$\tan x = \frac { \sqrt { 6 } } { 12 }$ 
B) 
$\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = - 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
C) 
$\cos x = \frac { 2 \sqrt { 6 } } { 5 }$ 
$\csc x = 5$
 $\tan x = - \frac { \sqrt { 6 } } { 12 }$ 
D) 
$\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
E) 
$\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
A) 
$\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = \frac { 1 } { 5 }
\end{array}$
$\tan x = \frac { \sqrt { 6 } } { 12 }$ 
B) 
$\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = - 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
C) 
$\cos x = \frac { 2 \sqrt { 6 } } { 5 }$ 
$\csc x = 5$
 $\tan x = - \frac { \sqrt { 6 } } { 12 }$ 
D) 
$\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
E) 
$\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$

Question 7

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

Accepted Answer

A)  $- 8 \cos x$ 
B)  $\frac { 1 } { 8 } \cos x$ 
C)  $8 \cos x$ 
D)  $8 \sin x$ 
E)  $- \frac { 1 } { 8 } \cos x$ 
A)  $- 8 \cos x$ 
B)  $\frac { 1 } { 8 } \cos x$ 
C)  $8 \cos x$ 
D)  $8 \sin x$ 
E)  $- \frac { 1 } { 8 } \cos x$

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

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.)

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

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

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

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

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Exam 5: Analytic Trigonometry

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​

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.)

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

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

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

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