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Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 9\) of a circle

Find the radian measure of four angles in standard position that are coterminal with the angle in stan- dard position whose measure is given. $$7 \pi / 5$$

Find the radian measure of four angles in standard position that are coterminal with the angle in stan- dard position whose measure is given. $$-\pi / 6$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$7 \pi / 4$$

(a) State the rule of a function of the form $$f(t)=A \sin (b t+c)$$ whose graph appears to be identical with the given graph. (b) State the rule of a function of the form $$g(t)=A \cos (b t+c)$$ whose graph appears to be identical with the given graph. (Check your book to see graph)

Use graphs to determine whether the equation could possibly be an identity or definitely is not an identity. $$\frac{\sin t}{1+\cos t}=\tan t$$

The brightness of the binary star Beta Lyrae (as seen from the earth) varies. Its visual magnitude \(M(t)\) after \(t\) days is approximately $$M(t)=.55 \cos (.97 t)+3.85$$ The visual magnitude scale is reversed from what you would expect: The lower the number, the brighter the star. With this in mind, answer the following questions. (a) Graph the function \(M\) when \(0 \leq t \leq 21\) (b) What is the visual magnitude when the star is brightest? When it is dimmest? (c) What is the period of the magnitude (the interval between its brightest times)?

The original Ferris wheel, built by George Ferris for the Columbian Exposition of \(1893,\) was much larger and slower than its modern counterparts: It had a diameter of 250 feet and contained 36 cars, each of which held 60 people; it made one revolution every 10 minutes. Imagine that the Ferris wheel revolves counterclockwise in the \(x-y\) plane with its center at the origin. A car had coordinates (125,0) at time \(t=0 .\) Find the rule of a function that gives the \(y\) -coordinate of the car at time \(t.\)

Determine the positive radian measure of the angle that the second hand of a clock traces out in the given time. 2 minutes and 15 seconds.

A pendulum swings uniformly back and forth, taking 2 seconds to move from the position directly above point \(A\) to the position directly above point \(B\). (Check your book to see image) The distance from \(A\) to \(B\) is 20 centimeters. Let \(d(t)\) be the horizontal distance from the pendulum to the (dashed) center line at time \(t\) seconds (with distances to the right of the line measured by positive numbers and distances to the left by negative ones). Assume that the pendulum is on the center line at time \(t=0\) and moving to the right. Assume that the motion of the pendulum is simple harmonic motion. Find the rule of the function \(d(t)\)