## Find the exact value of sin17pi/6...

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
starsound
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### Find the exact value of sin17pi/6...

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

1. sin$\frac{17\pi}{6}$
2. tan$\frac{13\pi}{4}$
3. sec$\frac{11\pi}{3}$

I am not sure how to approach this. I looked at the unit circle and know that all three of these go around the circle almost once or one time. Do I have to look at the reference angles for this? Also how does sin, tan and sec affect the answer?
I know tan (theta)=y/x, sec(theta)= 1/x and sin(theta)= y.

Thanks.

nona.m.nona
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### Re: Find the exact value of sin17pi/6...

To do these sorts of evaluations, the general idea is to reduce the angle to something in the first period, and then restate the angle in terms of the basic reference angles you've memorized so you can apply an identity.

For instance, (17pi)/6 = (12pi)/6 + (5pi)/6 = 2pi + (5pi)/6, so the sine of (17pi)/6 has the same value as the sine of (5pi)/6. From what you've learned of the sine wave, you know that the sine of (5pi)/6 has the same value (though the opposite sign) as the sine of pi/6. Use this to find the value of the given expression.

Follow the same sort of procedure for the other exercises.