Exam 5: Trigonometric Functions

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. - $\mathrm { r } = 22.1$ feet, $\theta = 11.19 ^ { \circ } , \mathrm { A } =$ ?

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

Find the phase shift of the function. - $y = 3 \cos \left( - 3 x - \frac { \pi } { 2 } \right)$

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\sin x = 0$ ?

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sin 67 ^ { \circ }$

Find the exact value of the expression. Do not use a calculator. - $\sin \frac { \pi } { 3 } - \cos \frac { \pi } { 6 }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\sin \theta = \frac { 1 } { 6 } , \quad \sec \theta < 0$ Find $\cos \theta$ and $\tan \theta$ .

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \sin ( 4 x + 3 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \tan \theta \quad$ Find $f ( \theta )$ .

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ - $6 ^ { \circ }$

Match the function to its graph. - $y = - \tan ( x + \pi )$

Solve the problem. -Determine the sign of the trigonometric values listed below. (i) $\sin 250 ^ { \circ }$ (ii) $\tan 330 ^ { \circ }$ (iii) $\cos \left( - 40 ^ { \circ } \right)$

Graph the function. Show at least one period. - $y=4 \sin (-2 x-\pi)$ A) B) C) D)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin \frac { 11 \pi } { 3 }$

Solve the problem. - $\text { If } f ( \theta ) = \sin \theta \text { and } f ( a ) = - \frac { 1 } { 9 } \text {, find the exact value of } f ( a ) + f ( a - 4 \pi ) + f ( a - 2 \pi )$

Solve the problem. -The current I, in amperes, flowing through a particular ac (alternating current) circuit at time t seconds is $I = 220 \sin ( 65 \pi t )$ What is the period and amplitude of the current? A) period $= \frac { \pi } { 120 }$ second, amplitude $= 60$ B) period $= \frac { 1 } { 30 }$ second, amplitude $= 120$ C) period $= 60 \pi$ seconds, amplitude $= \frac { 1 } { 30 }$ D) period $= \frac { 1 } { 480 }$ second, amplitude $= 480$

Solve the problem. -A car is traveling at 50 mph. If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\sin x = 1$ ?

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

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