Exam 6: The Circular Functions and Their Graphs

Solve the problem. -Let angle $P O Q$ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 45 ^ { \circ }$ , find the exact length of $P Q$ .

Solve the problem. -A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 6 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Find the phase shift of the function. - $y = - 5 - 3 \sin \left( 5 x - \frac { \pi } { 2 } \right)$

Solve the problem. -Find $\omega$ for the minute hand of a clock.

Solve the problem. -Determine the length of a pendulum that has a period of 2 seconds.

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 6.4 \mathrm { mi } , \theta = 36 ^ { \circ }$

Find the exact circular function value. - $\cos \frac { - 2 \pi } { 3 }$

Solve the problem. -Use regression to find constants $a , b , c$ , and d so that $\mathrm { f } ( \mathrm { x } ) = \mathrm { a } \sin ( \mathrm { bx } + \mathrm { c } ) + \mathrm { d }$ models the data given below. Round all answers to 9 decimal places.

Convert the degree measure to radians. Leave answer as a multiple of π. - $630 ^ { \circ }$

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. -sec $s = 2.2426$

Find the exact circular function value. - $\cos 2 \pi$

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π. -2

Solve the problem. -Let angle $P O Q$ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 45 ^ { \circ }$ , find the exact length of OU.

Find the exact circular function value. - $\sec \frac { 5 \pi } { 4 }$

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

Convert the degree measure to radians. Leave answer as a multiple of π. - $390 ^ { \circ }$

Graph the function. - $y = 2 \sin \left( x + \frac { \pi } { 3 } \right)$

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find $\tan \theta$ .

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin \frac { 1 } { 3 } x$