Exam 5: Trigonometric Functions

Match the given function to its graph. -1) $y = \sin 3 x$ 2) $y = 3 \cos x$ 3) $y = 3 \sin x$ 4) $y = \cos 3 x$

Solve the problem. -The following data represents the normal monthly precipitation for a certain city in Arkansas. Month, x Normal Monthly Precipitation, inches January, 1 3.91 February, 2 4.36 March, 3 5.31 April, 4 6.21 May, 5 7.02 June, 6 7.84 July, 7 8.19 August, 8 8.06 September, 9 7.41 October, 10 6.30 November, 11 5.21 December, 12 4.28 Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram. that

Name the quadrant in which the angle θ lies. - $\tan \theta > 0 , \quad \sin \theta < 0$

Match the function to its graph. - $y = - \tan x$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - 30 ^ { \circ } \right)$

Find an equation for the graph. -

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

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. -6.46

Solve the problem. -For what numbers $x , - 2 \pi \leq x \leq 2 \pi$ , does the graph of $y = \tan x$ have vertical asymptotes.?

Solve the problem. -An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object? A) $2 \mathrm {~m} / \mathrm { sec }$ В) $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$ C) $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$ D) $3 \mathrm {~m} / \mathrm { sec }$

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

Choose the one alternative that best completes the statement or answers the question. -A pendulum swings though an angle of 20° each second. If the pendulum is 35 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places.

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ -160° A) $\frac { 7 \pi } { 8 }$ B) $\frac { 8 \pi } { 9 }$ C) $\frac { 9 \pi } { 10 }$ D) $\frac { 9 \pi } { 8 }$

Solve the problem. -A carousel has a radius of 15 feet and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places.

Graph the function. - $y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$ A) B) C) D)

Match the given function to its graph. -1) $y = \sin x$ 2) $y = \cos x$ 3) $y = - \sin x$ 4) $y = - \cos x$

Name the quadrant in which the angle θ lies. - $\cot \theta < 0 , \quad \cos \theta > 0$

Graph the function. - $y = \frac { 1 } { 3 } \cot \left( x - \frac { \pi } { 4 } \right)$ A) B) C) D)

Find an equation for the graph. - A) $y = 4 \cos \left( \frac { \pi } { 3 } x \right)$ B) $y = 3 \cos \left( \frac { \pi } { 5 } x \right)$ C) $y = 3 \cos ( 5 \pi x )$ D) $y = 5 \cos ( 3 \pi x )$