How do you evaluate $tan (arccos (- \frac{3}{4}))$ $tan(arccos(-3/4))$ without a calculator?

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How do you evaluate $tan (arccos (- \frac{3}{4}))$ $tan(arccos(-3/4))$ without a calculator?

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Answer 1 · 2016-08-10T07:49:29

$- \frac{\sqrt{7}}{3}$ $-sqrt 7/3$

Explanation:

Let $a = a r c cos (- \frac{3}{4}) \in Q 2$ $a = arc cos (-3/4) in Q2$ , wherein tangent is also negative.

Then, the given expression is

$tan a = \frac{sin a}{cos a} = - \frac{\sqrt{1 - {(- \frac{3}{4})}^{2}}}{- \frac{3}{4}} = - \frac{\sqrt{7}}{3}$ $tan a = sin a/cos a=-sqrt(1-(-3/4)^2)/(-3/4)=-sqrt 7/3$

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How do you evaluate $tan (arccos (- \frac{3}{4}))$ $tan(arccos(-3/4))$ without a calculator?

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Explanation:

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How do you evaluate $tan (arccos (- \frac{3}{4}))$ $tan(arccos(-3/4))$ without a calculator?