Exam 15: Trigonometric Functions Web

From the given function $\cos \theta = \frac { 4 } { 5 }$ , find the following trigonometric function. $\sin \theta$

Find the period and amplitude of the function $y = 3 \cos 2 x$ .

Find the derivative of the function. $y = 2 \cos 5 x$

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 = $\frac { \sqrt { 2 } } { 2 }$

Find the radian measure of the given angle. 750o

Evaluate without using a calculator. $\tan \frac { \pi } { 4 }$

Match the function below with the correct graph. $y = \sin x$

Determine the relative extrema of the function $y = 2 \cos x + \sin 2 x$ on the interval $( 0,2 \pi )$ .

Find the indefinite integral of the following function. $\int 4 x ^ { 3 } \cos x ^ { 4 } d x$

Evaluate without using a calculator, leaving the answers in exact form. $\sin \frac { 3 \pi } { 4 }$

Find the derivative of the function. $f ( \theta ) = \frac { 3 } { 7 } \sin ^ { 2 } 3 \theta$

Solve the triangle for the indicated side and angle.

Find $\sin \theta$ given that $\sec \theta = 4$ and $0 < \theta < \frac { \pi } { 2 }$ .

Suppose that the numbers W (in thousands) of construction workers employed in the United States during 2006 can be modeled by $W = 9094 + 455.2 \sin ( 0.6 t - 1.813 )$ where t is the time in months, with $t = 1$ corresponding to January 1. Approximate the month t in which the number of construction workers employed was a maximum. What was the maximum number of construction workers employed? Round your answer to nearest hundredth.

A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure). For a circle of radius $r,$ the area $A$ of a sector of the circle with central angle $\theta$ (measured in radians) is given by $A = \frac { 1 } { 2 } r ^ { 2 } \theta$ . A sprinkler system on a farm is set to spray water over a distance of $60$ feet and rotates through an angle of $110 ^ { \circ }$ . Use the above given information to find the area of the region. Round your answer to two decimal places.

A 20-foot ladder leaning against the side of a house makes a 75 $^\circ$ angle with the ground (see figure). How far up the side of the house does the ladder reach? Round your answer to four decimal places.

Evaluate without using a calculator, leaving the answers in exact form. $\cos \frac { 2 \pi } { 3 }$

Use a calculator to evaluate the trigonometric function $\cos 400 ^ { \circ }$ to four decimal places.

A compact disc can have an angular speed up to 3146 radians per minute. At this angular speed, how many revolutions per minute would the CD make? Round your answer to the nearest integer.

Determine the quadrant in which $\theta$ lies if sin q < 0 and cos q > 0.