Learning Objectives
By the end of this section, you will be able to:
- Find function values for the sine and cosine of [latex]30^\circ \text{ or }\left(\frac{\pi }{6}\right),45^\circ \text{ or }\left(\frac{\pi }{4}\right)[/latex] and [latex]{60^\circ }^{}\text{or}\left(\frac{\pi }{3}\right)[/latex].
- Identify the domain and range of sine and cosine functions.
- Use reference angles to evaluate trigonometric functions.
Figure 1. The Singapore Flyer is the world’s tallest Ferris wheel. (credit: “Vibin JK”/Flickr)
Looking for a thrill? Then consider a ride on the Singapore Flyer, the world’s tallest Ferris wheel. Located in Singapore, the Ferris wheel soars to a height of 541 feet—a little more than a tenth of a mile! Described as an observation wheel, riders enjoy spectacular views as they travel from the ground to the peak and down again in a repeating pattern. In this section, we will examine this type of revolving motion around a circle. To do so, we need to define the type of circle first, and then place that circle on a coordinate system. Then we can discuss circular motion in terms of the coordinate pairs.