91Ó°ÊÓ

In Exercises 37-44, evaluate the trigonometric function of the quadrant angle. \(sec\ \pi\)

In Exercises 35-42, evaluate the trigonometric function using its period as an aid. cos \((-\frac{9\pi}{4})\)

In Exercises 37-46, use trigonometric identities to transform the left side of the equation into the right side \((0\ <\ \theta\ <\ \pi /2)\). sin\(^2\) \(\theta\) \(-\) cos\(^2\) \(\theta = 2\) sin\(^2 \theta - 1\)

GEOMETRY Find the length of the sides of a regular hexagon inscribed in a circle of radius 25 inches.

HARMONIC MOTION In Exercises 53-56, find a model for simple harmonic motion satisfying the specified conditions. \(Displacement\ (t=0)\) 0 \(Amplitude\) 4 centimeters \(Period\) 2 seconds

In Exercises 55-66, find the exact value of the expression. (Hint:Sketch a right triangle.) \(cos(tan^{-1}\ 2)\)

In Exercises 53-68, evaluate the sine, cosine, and tangent of the angle without using a calculator. \(\frac{2\pi}{3}\)

TUNING FORK A point on the end of a tuning fork moves in simple harmonic motion described by \(d=a\ sin\ \omega t\). Find \(\omega\) given that the tuning fork for middle C has a frequency of 264 vibrations per second.

In Exercises 57-62, find the values of \(\theta\) in degrees \((0^\circ\ <\ \theta\ <\ 90^\circ)\) and radians \((0\ <\ \theta\ <\ \pi/2)\) without the aid of a calculator. (a) csc \(\theta\ = \frac{2\sqrt{3}}{3}\) (b) sin \(\theta\ = \frac{\sqrt{2}}{2}\)

WAVE MOTION A buoy oscillates in simple harmonic motion as waves go past. It is noted that the buoy moves a total of 3.5 feet from its low point to its high point (see figure), and that it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy if its high point is at \(t=0\).