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Find the exact value of cos (17π/6) by using the unit circle.

Find the exact value of cos (17π/6) by using the unit circle.-example-1
User Snksnk
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It is required to find the exact value of 17π/6 using the unit circle.

To do this, locate the angle on the unit circle to determine the point (x,y) it represents.

Recall that on the unit circle, the cosine is:


\cos\theta=x

Since 17π/6 is greater than 2π, find its equivalent angle that is less than 2π by subtracting multiples of 2π until it is less than 2π:


(17\pi)/(6)-2\pi=(5\pi)/(6)

Locate this point on the unit circle:

From the unit circle, it can be seen that:


x=-(√(3))/(2)\text{ and }y=(1)/(2)

Hence, the required value is:


\cos(17\pi)/(6)=-(√(3))/(2)

The answer is the first option.

Find the exact value of cos (17π/6) by using the unit circle.-example-1
User Jimmu
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