QuestionFind the values of: (a) $\sin \frac{\pi}{3}$ , (b) $\cos \frac{2 \pi}{3}$ , and $\tan \frac{7 \pi}{4}$ in surd form.

Studdy Solution

STEP 1

Assumptions1. We are dealing with trigonometric functions sine, cosine and tangent. . The values of these functions are given in terms of $\pi$ .
3. We are required to provide the values in surd form if necessary.

STEP 2

(a) We need to find the value of $\sin \frac{\pi}{}$ .This is a standard value in trigonometry. The sine of $\frac{\pi}{}$ is $\frac{\sqrt{}}{2}$ .
So, $\sin \frac{\pi}{} = \frac{\sqrt{}}{2}$ .

STEP 3

(b) We need to find the value of $\cos \frac{2 \pi}{3}$ .
This is also a standard value in trigonometry. The cosine of $\frac{2\pi}{3}$ is $-\frac{1}{2}$ .
So, $\cos \frac{2 \pi}{3} = -\frac{1}{2}$ .

STEP 4

(c) We need to find the value of $\tan \frac{7 \pi}{4}$ .
This is a standard value in trigonometry. The tangent of $\frac{7\pi}{4}$ is $1$ .
So, $\tan \frac{7 \pi}{4} =1$ .
The values of the trigonometric functions are(a) $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$ (b) $\cos \frac{2 \pi}{3} = -\frac{1}{2}$ (c) $\tan \frac{7 \pi}{4} =1$

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