Exam 4: Graphs of the Circular Functions

Solve the problem. -For an electrical circuit, the voltage $E$ is modeled by $E = 2.7 \cos 38 \pi t$ , where $t$ is the time in seconds. How many cycles are completed in one second?

Graph the function. - $y=-3 \cos x$

Determine the equation of the graph. -

Graph the function. - $y = \frac { 1 } { 2 } \cos \frac { 1 } { 3 } x$

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. - $y = \cos \left( x - \frac { \pi } { 3 } \right)$

Solve the problem. -The chart represents the amount of fuel consumed by a machine used in manufacturing. The machine is turned on at the beginning of the day, takes a certain amount of time to reach its full Power (the point at which it uses the most fuel per hour), runs for a certain number of hours, and is Shut off at the end of the work day. The fuel usage per hour of the machine is represented by a Periodic function. When does the machine first reach its full power?

Graph the function. - $y=3 \sin \left(x-\frac{\pi}{4}\right)$

Graph the function. - $y=-2 \sin x$

Determine the equation of the graph. A) $y = - 4 + \sec x$ B) $y = - 4 + \sec 4 x$ C) $y = - 4 - \csc x$ D) $y = - 4 + \csc x$ -Determine the equation of the graph.

Give the amplitude or period as requested. -Period of $y = \cos 5 x$

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 guitar string is plucked so that it vibrates with a frequency of F = 66. Suppose the maximum displacement at the center of the string is s(0)= 0.58. Find an equation of the form s(t)= a cos bt to Model this displacement. Round constants to 2 decimal places.

Solve the problem. -Use regression to find constants a, b, c, and d so that f(x)= a sin (bx + c)+ d models the data given below. Round all answers to 9 decimal places. Month 1 2 3 4 5 6 7 8 9 10 11 12 Precipitation (inches) 1 3 6 9 11 12 11 9 7 5 3 2

Find the specified quantity. -Find the amplitude of $y = - 2 \cos ( 4 x - \pi )$ .

Match the function with its graph. -1) y = sin 3x 2) y = 3 cos x 3) y = 3 sin x 4) y = cos 3x a) b) c) d)

Solve the problem. -The path of a projectile fired at an inclination $\theta$ to the horizontal with an initial speed $v _ { O }$ is a parabola. The range $\mathrm { R }$ of the projectile, the horizontal distance that the projectile travels, is found by the formula $\mathrm { R } = \frac { \mathrm { v } _ { \mathrm { O } } ^ { 2 } \sin 2 \theta } { \mathrm { g } }$ where $\mathrm { g } = 32.2$ feet per second per second or $\mathrm { g } = 9.8$ meters per second per second. Find the range of a projectile fired with an initial velocity of 140 feet per second at an angle of $27 ^ { \circ }$ to the horizontal. Round your answer to two decimal places.

Graph the function. - $y=\frac{2}{3} \sin \frac{1}{2} x$

Solve the problem. -A coil of wire rotating in a magnetic field induces a voltage given by $e = 20 \sin \left( \frac { \pi t } { 4 } - \frac { \pi } { 2 } \right)$ where $t$ is time in seconds. Find the smallest positive time to produce a voltage of $10 \sqrt { 2 }$ .

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