Question

Evaluate sin(cos^-1(-15/17))

Answer 1

cos⁻¹ a = arccos a

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sin(cos⁻¹ (-15/17)) = sin(arccos(-15/17))

$sin(arccos(x))=\sqrt{1-x^{2}}$

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$sin(arccos(-\frac{15}{17})=\sqrt{1-(-\frac{15}{17})} =\sqrt{1-\frac{225}{289}} =\sqrt{\frac{64}{289}} =\frac{8}{17}$

ANSWER : 8/17

Answer 2

Hello!

First of all, let's find the arcosine (cos^-1) of (-15/17)

cos^-1(-15/17)≈-28.1

Now we find the sine of this number.

sin-28.1≈0.47

Therefore, our answer is about 0.47

I hope this helps!