Exam 5: Trigonometric Functions

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 sect.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 72 ^ { \circ }$

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

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

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( 4 , - 3 )$ Find $\cos \theta .$

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

Find the phase shift of the function. - $y = - 3 \cos ( 4 x + \pi )$

Solve the problem. -If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 6$ , find the exact value of $f ( - a )$ .

Draw the angle. - $\frac { 7 \pi } { 4 }$

Without graphing the function, determine its amplitude or period as requested. - $y = \frac { 3 } { 4 } \sin \left( - \frac { 4 \pi } { 5 } x \right) \quad$ Find the amplitude.

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. - $\mathrm { r } = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $\mathrm { A } =$ ?

Choose the one alternative that best completes the statement or answers the question. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\cot \theta$

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

Solve the problem. -If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 4$ , find the exact value of $f ( a ) + f ( a + \pi ) + f ( a + 3 \pi )$ .

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

Choose the one alternative that best completes the statement or answers the question. -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?

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of $60 ^ { \circ }$ . Round to the nearest hundredth.

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $\mathrm { g } ( \theta ) = \cos \theta \quad$ Find $12 \mathrm {~g} ( \theta )$ .

Choose the one alternative that best completes the statement or answers the question. -A pendulum swings though an angle of $20 ^ { \circ }$ 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.

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