Exam 15: Trigonometric Functions Web

Solve the equation below for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\sin 2 \theta - \cos \theta = 0$

Find two values of q that satisfy the equation below. Give values of q in radians $( 0 \leq \theta \leq 2 \pi )$ . Do not use a calculator. sin q = $- \frac { \sqrt { 3 } } { 2 }$

Use integration by parts to find the indefinite integral. $\int x \cos 2 x d x$

Find the derivative of the function $y = \ln \left( \cos ^ { 2 } x \right)$ and simplify your answer by using the trigonometric identities.

Solve the equation below for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\cos ^ { 2 } \theta + \sin \theta = 1$

Find the period of the trigonometric function. $y = \cot \frac { \pi x } { 6 }$

Find the derivative of the function and simplify your answer by using the trigonometric identities $y = \cos ^ { 2 } x$

Find the degree measure of the given angle. $\frac { 4 \pi } { 7 }$

Find a and d for $f ( x ) = a \cos x + d$ such that the graph of f matches the figure.

Find the radian measure of the given angle. 225o

Find the indefinite integral. $\int \tan ^ { 3 } x \sec ^ { 2 } x d x$

Evaluate the definite integral. $\int _ { 0 } ^ { \pi / 4 } 4 \sec ^ { 2 } 3 t c t$

Approximate using a calculator (set for radians). Round answers to two decimal places. $\sin 2$

A guy wire is stretched from a broadcasting tower at a point 300 feet above the ground to an anchor 175 feet from the base (see figure). How long is the wire?

Find the cosine of $\theta$ .

Solve the triangle for the indicated side.

Find the indefinite integral of the following function. $\int \cos 2 t d t$

Solve the triangle for the indicated angle.

Solve the equation for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\cos 2 \theta + 3 \cos \theta + 2 = 0$

The average monthly precipitation P (in inches), including rain, snow, and ice, for Sacramento, California can be modeled by $P = 2.47 \sin ( 0.40 t + 1.80 ) + 2.08,$ $0 \leq t \leq 12$ where $t$ is the time (in months), with $t = 1$ corresponding to January. Find the total annual precipitation for Sacramento.