Exam 6: The Circular Functions and Their Graphs

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, $30 ^ { \circ } \mathrm { N }$ , are $2234 \mathrm {~km}$ apart.

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π. - $- 6.8$

Find the exact circular function value. - $\tan \frac { - 3 \pi } { 4 }$

Match the function with its graph. -1) $y = \sin \left( x - \frac { \pi } { 2 } \right)$ 2) $y = \cos \left( x + \frac { \pi } { 2 } \right)$ 3) $y = \sin \left( x + \frac { \pi } { 2 } \right)$ 4) $y = \cos \left( x - \frac { \pi } { 2 } \right)$ A. B. C. D.

Find the exact values of s in the given interval that satisfy the given condition. - $[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$

Find the phase shift of the function. - $y = - 4 + 2 \sin \left( 3 x + \frac { \pi } { 4 } \right)$

Solve the problem. -Two pulleys of diameters $6 \mathrm {~m}$ and $3 \mathrm {~m}$ are connected by a belt. The larger pulley rotates 44 times per min. Find the angular speed of the smaller pulley.

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

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. -

Solve the problem. -Write the equation that describes the simple harmonic motion of a particle moving uniformly around a circle of radius 7 units, with angular speed 2 radians per second.

Graph the function over a one-period interval. - y=-4(x-\pi)

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

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

Match the function with its graph. -1) $y = \sin x$ 2) $y = \cos x$ 3) $y = - \sin x$ 4) $y = - \cos x$ A. B. C. D.

Solve the problem. -A pendulum of length $\mathrm { L }$ , when displaced horizontally and released, oscillates with harmonic motion according to the equation $\mathrm { y } = \mathrm { A } \sin ( ( \sqrt { \mathrm { g } / \mathrm { L } } ) \mathrm { t } + \pi / 2 )$ , where $\mathrm { y }$ is the distance in meters from the rest position $t$ seconds after release, and $g = 9.8 \mathrm {~m} / \mathrm { sec } ^ { 2 }$ . Identify the period, amplitude, and phase shift when $\mathrm { A } = 0.28 \mathrm {~m}$ and $\mathrm { L } = 1.96 \mathrm {~m}$ . Round all answers to the nearest hundredth.

Solve the problem. -A pulley rotates through $63 ^ { \circ }$ in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make in an hour?

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. - $\mathrm { r } = 18.1 \mathrm {~cm} , \theta = \frac { \pi } { 7 }$ radians

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. - $\mathrm { r } = 6.0 \mathrm {~m} , \theta = 20 ^ { \circ }$

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. -

Solve the problem. -A weight attached to a spring is pulled down 9 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.