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Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 7.3 Unit Circle

Calculating Sines and Cosines along an Axis

Find $cos (90°)$ and $sin (90°) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Moving $90°$ counterclockwise around the unit circle from the positive x-axis brings us to the top of the circle, where the $(x, y)$ coordinates are $90°$ as shown in Figure 6.

Figure 6

We can then use our definitions of cosine and sine.

$\begin{matrix} x & = cos t & = \cos (90°) & = 0 \\ y & = sin t & = \sin (90°) & = 1 \end{matrix}$
The cosine of $90°$ is 0; the sine of $90°$ is 1.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find cosine and sine of the angle $π .$

How did it go?

PreviousFinding Function Values for Sine and Cosine Next Finding a Cosine from a Sine or a Sine from a Cosine

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.