For each angle, find two angles that are coterminal with it.

a. 135\(^{\circ}\) b. \(-60\) \(^{\circ}\)

A vintage vinyl record makes 45 revolutions per minute. What is the linear speed of point 3 inches from the center? See Fuigure 17.

In a bicycle race, on of the bicyclists travels at a speed of 40 kilometers per hour. If the diameter of the bicycle wheel is 0.66 meters, find the angular speed of the wheel in

a. radians per hour.

b. revolutions per hour.

Find the sine and cosine of the following angle

a. t = 0

b. t = \(\displaystyle\frac{3\pi}{2}\)

FInd the exact values of cos \(\displaystyle\frac{\pi}{6}\) and sin\(\displaystyle\frac{\pi}{6}\).

Find the values of the trignometric functions of \(\frac{\pi}{3}\) to complete Table 4.

Use the triangle in Frigure 3 to find the six trigonometric functions of \(\theta\).

A surveyor stands 100 feet from the base of a building. From that point, the angle of elevation to the top of the building is 78 \(^{\circ}\). See Figure 13. Find the height of the building. Round your answer to two decinal places.

An observer meansures an angle of elevation of 41 \(^{\circ}\) to the top of a lighthouse from a certain point on the ground. She then walks 15 feet closer to the lighthouse and measures an angle of elevaion of 44\(^{\circ}\). See Figure 15. How tall is the lighthouse? Round your answer to two decimal places.

In Figure 2 and Figure 3, find the exact values of all the trigonometric functions of each value of \(\theta\).

Find

a. sin 480\(^{\circ}\)

b. cos (\(-90\) \(^{\circ}\))

A ramp is to be constructed with a slope of \(\displaystyle\frac{1}{10}\). See Figure 12. Find the acute angle that the ramp makes with the horizontal. Express the angle in degrees.