Exam 5: Trigonometric Functions

Use transformations to graph the function. - $y=-3 \cos x$ A) B) C) D)

Solve the problem. - $\text { Is the function } \mathrm { f } ( \theta ) = \sin \theta + \cos \theta \text { even, odd, or neither? }$

Find the area A. Round the answer to three decimal places. -

Solve the problem. -If $\tan \theta = - 0.4$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Draw the angle. - $- \frac { 7 \pi } { 6 }$

Graph the function. - $y=2 \sec (3 x)$ A) B) C) D)

Find the exact value. Do not use a calculator. - $\cot \frac { \pi } { 6 }$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = 60 ^ { \circ } , \mathrm { A } = 100 \text { square meters, } \mathrm { r } = \text { ? }$

Graph the function. - $y=-\cot (\pi x)$ A) B) C) D)

Choose the one alternative that best completes the statement or answers the question. -The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places.

Convert the angle in radians to degrees. - $\frac { 7 \pi } { 12 }$

Solve the problem. -What is the range of the tangent function?

Without graphing the function, determine its amplitude or period as requested. - $y = 4 \sin x \quad$ Find the amplitude.

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { \sqrt { 7 } } { 4 } , \frac { 3 } { 4 } \right)$ Find $\sec t$ .

Graph the function. - $y=\csc \left(\frac{\pi x}{5}+\frac{3 \pi}{5}\right)$ A) B) C) D)

Find the exact value. Do not use a calculator. - $\sec \frac { 13 \pi } { 4 }$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( - \frac { \sqrt { 33 } } { 7 } , - \frac { 4 } { 7 } \right)$ Find $\sin \mathrm { t }$

Draw the angle. -330° A) B) C) D)

Solve the problem. -The average daily temperature T of a city in the United States is approximated by $T = 55 - 23 \cos \frac { 2 \pi } { 365 } ( t - 30 )$ where t is in days, $1 \leq \mathrm { t } \leq 365 \text {, }$ nd t = 1 corresponds to January 1. Find the period of T.

Find an equation for the graph. - A) $y = - 4 \cos \left( \frac { 1 } { 3 } x \right)$ B) $y = - 4 \sin \left( \frac { 1 } { 3 } x \right)$ C) $y = - 4 \cos ( 3 x )$ D) $y = - 4 \sin ( 3 x )$