Exam 3

1. Find the length s and area A.

2.  The variable t is a real​ number, and

  is the point on the unit circle that corresponds to t. Find the exact values of the six trigonometric functions of t

3. The point given below is on the terminal side of an angle

 in standard position. Find the exact value of each of the six trigonometric functions of 

(8, -3)

4.  Find the exact value of each of the remaining trigonometric functions of

.

$\sin \theta =\frac{4}{5},\theta in quadrant I$

5. Graph the function

  . Show at least two cycles. Use the graph to determine the domain and range of the function.

6.  Graph the following function. Show at least two cycles. Use the graph to determine the domain and range of the function.

y = -2 tan x

7.  Find the exact​ value, if​ any, of the following composite function. Do not use a calculator.

${\sin }^{–1}(\sin \frac{6\mathrm{\pi }}{7})$

8.  Find the exact​ value, if​ any, of the following composite function. If there is no​ value, say it is​ “not defined.” Do not use a calculator.

${\tan }^{–1} \left[\tan \left(\frac{7\mathrm{\pi }}{2}\right)\right]$

9.  Find the exact value of the expression.

${\cos }^{–1}\left[\tan \left(\frac{\mathrm{\pi }}{4}\right)\right]$

10.   Find the exact value of the expression.

$sec \left[{\tan }^{–1}\left(\frac{4}{9}\right)\right]$

11.  Solve the equation on the interval

$$\begin{gathered} 0\le \theta <2\mathrm{\pi } \\ 2 {\cos }^2\mathrm{\theta } – \sqrt{3}\cos \mathrm{\theta } = 0 \end{gathered}$$

12. Solve the equation.

$3 – 3 \sin \theta = 6 {\cos }^2 \theta$

13 .  Use a sum or difference formula to find the exact value of the trigonometric function.

cos 165

14. Find the value of each of the six trigonometric functions of the angle

 in the figure.

15.  A building that is 280  feet tall casts a shadow 40 feet long. What is the angle of elevation of the​ Sun?