Exam 5: Trigonometric Functions

Graph the sinusoidal function. - $y=-3 \cos (\pi x)$ A) B) C) D)

Solve the problem. -If $\sin \theta = 0.7$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $127 ^ { \circ } 58 ^ { \prime } 55 ^ { \prime \prime }$

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

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\sec ^ { 2 } 40 ^ { \circ } - \tan ^ { 2 } 40 ^ { \circ }$

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $4 \pi$ Phase Shift: $\frac { \pi } { 4 }$

Find the exact value. Do not use a calculator. - $\cot 570 ^ { \circ }$

Match the given function to its graph. -1) $y = \sin \left( \frac { 1 } { 3 } x \right)$ 2) $y = \frac { 1 } { 3 } \cos x$ 3) $y = \frac { 1 } { 3 } \sin x$ 4) $y = \cos \left( \frac { 1 } { 3 } x \right)$

Write the equation of a sine function that has the given characteristics. -Amplitude: 2 Period: $\pi$ Phase Shift: $\frac { 7 } { 2 }$

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ - $87 ^ { \circ }$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 3 , - 2 ) \quad$ Find $\tan \theta$ .

Graph the function. - $y=-2 \cot (4 x)$ A) B) C) D)

Graph the sinusoidal function. - $y=4 \sin (\pi x)$ A) B) C) D)

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $23 ^ { \circ } 47 ^ { \prime } 37 ^ { \prime \prime }$

Find the exact value. Do not use a calculator. - $\cos \pi$

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

Graph the function. - $y = - \tan \left( x - \frac { \pi } { 4 } \right)$ A) B) C) D)

Find an equation for the graph. - A) $y = 3 \cos \left( \frac { 1 } { 2 } x \right)$ B) $y = 3 \cos ( 2 x )$ C) $y = 2 \cos ( 3 x )$ D) $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\tan 930 ^ { \circ }$

Solve the problem. -The four Galilean moons of Jupiter have orbital periods and mean distances from Jupiter given by the following table. Distance () Period (Earth hours) Io 4.214\times1 42.460 Europa 6.709\times1 85.243 Ganymeade 1.070\times1 171.709 Callisto 1.883\times1 400.536 Find the linear speed of each moon. Which is the fastest (in terms of linear speed)?