Question

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find this value.

17π
Sin-------
6

13π
tan------
4

11π
sec-------
3

Answer 1

Answer on Question #57974– Math– Trigonometry

Question

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find this value.

17π

Sin---

6

13π

tan---

4

11π

sec---

3

Solution

$$\sin \frac{17\pi}{6} = \sin \left(2\pi + \frac{5\pi}{6}\right) = |2\pi \text{ is the period of the sine function}| = \sin \left(\frac{5\pi}{6}\right) = \sin \left(\pi - \frac{\pi}{6}\right) = \sin \left(\frac{\pi}{6}\right) = \frac{1}{2},$$ $$\tan \frac{13\pi}{4} = \tan \left(3\pi + \frac{\pi}{4}\right) = \tan \left(\pi + \pi + \pi + \frac{\pi}{4}\right) = | \pi \text{ is the period of the tangent function} | = \tan \left(\frac{\pi}{4}\right) = 1,$$ $$\sec \left(\frac{11\pi}{3}\right) = \frac{1}{\cos \left(\frac{11\pi}{3}\right)} = \frac{1}{\cos \left(3\pi + \frac{2\pi}{3}\right)} = \frac{1}{\cos \left(2\pi + \pi + \frac{2\pi}{3}\right)} = |2\pi \text{ is the period of the cosine function}| = \frac{1}{\cos \left(\pi + \frac{2\pi}{3}\right)} = -\frac{1}{\cos \left(\frac{2\pi}{3}\right)} = -\frac{1}{-\frac{1}{2}} = 2.$$

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