Chapter 4

Find the exact value of each expression. $$\sin ^{-1} \frac{1}{2}$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(-4,3)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=4 \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$135^{\circ}$$

Find the exact value of each expression. $$\sin ^{-1} 0$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(-12,5)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=5 \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$177^{\circ}$$

Find the exact value of each expression. $$\sin ^{-1} \frac{\sqrt{2}}{2}$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(2,3)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=\frac{1}{3} \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$83.135^{\circ}$$

Find the exact value of each expression. $$\sin ^{-1} \frac{\sqrt{3}}{2}$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(3,7)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=\frac{1}{4} \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$87.177^{\circ}$$

Find the exact value of each expression. $$\sin ^{-1}\left(-\frac{1}{2}\right)$$

Graph two periods of the given tangent function. $$y=3 \tan \frac{x}{4}$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(3,-3)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=-3 \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$\pi$$

Find the exact value of each expression. $$\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Graph two periods of the given tangent function. $$y=2 \tan \frac{x}{4}$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(5,-5)$$

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=-4 \sin x$$

The measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. $$\frac{\pi}{2}$$

Find the exact value of each expression. $$\cos ^{-1} \frac{\sqrt{3}}{2}$$

Graph two periods of the given tangent function. $$y=\frac{1}{2} \tan 2 x$$

Determine the amplitude and period of each function. Then graph one period of the function. $$y=\sin 2 x$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(-2,-5)$$

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). Radius, \(r\) 10 inches Arc Length, \(s\) 40 inches

Determine the amplitude and period of each function. Then graph one period of the function. $$y=\sin 4 x$$

Find the exact value of each expression. $$\cos ^{-1} \frac{\sqrt{2}}{2}$$

Graph two periods of the given tangent function. $$y=2 \tan 2 x$$

In Exercises \(1-8,\) a point on the terminal side of angle \(\theta\) is given. Find the exact value of each of the six trigonometric functions of \(\theta\). $$(-1,-3)$$

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). Radius, \(r\) 5 feet Arc Length, \(s\) 30 feet

Determine the amplitude and period of each function. Then graph one period of the function. $$y=3 \sin \frac{1}{2} x$$

Find the exact value of each expression. $$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$$

Graph two periods of the given tangent function. $$y=-2 \tan \frac{1}{2} x$$

In Exercises \(9-16\), evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. $$\cos \pi$$

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). Radius, \(r\) 6 yards Arc Length, \(s\) 8 yards

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. (figure cannot copy) $$a=10.8, b=24.7$$

Determine the amplitude and period of each function. Then graph one period of the function. $$y=2 \sin \frac{1}{4} x$$

Graph two periods of the given tangent function. $$y=-3 \tan \frac{1}{2} x$$

Find the exact value of each expression. $$\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

In Exercises \(9-16\), evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. $$\tan \pi$$

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). Radius, \(r\) 8 yards Arc Length, \(s\) 18 yards

Determine the amplitude and period of each function. Then graph one period of the function. $$y=4 \sin \pi x$$

Graph two periods of the given tangent function. $$y=\tan (x-\pi)$$

Find the exact value of each expression. $$\cos ^{-1} 0$$