How do you find the exact value of $sin ({tan}^{- 1} - \frac{5}{7})$ $sin(tan^-1 -5/7)$ ?

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How do you find the exact value of $sin ({tan}^{- 1} - \frac{5}{7})$ $sin(tan^-1 -5/7)$ ?

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Answer 1 · 2017-01-13T11:02:25

$- \frac{5}{\sqrt{74}}$ $-5/sqrt74$

Explanation:

${tan}^{- 1} (- \frac{5}{7}) = {sin}^{- 1} (- \frac{5}{\sqrt{5^{2} + 7^{2}}}) = {sin}^{- 1} (- \frac{5}{\sqrt{74}})$ $tan^(-1)(-5/7)= sin^(-1)(-5/sqrt(5^2+7^2))=sin^(-1)(-5/sqrt74)$

The given expression is

$sin ({sin}^{- 1} (- \frac{5}{\sqrt{74}})) = - \frac{5}{\sqrt{74}}$ $sin(sin^(-1)(-5/sqrt74))=-5/sqrt74$ .

Note that , if arc tan is negative, the angle is in $Q_{4}$ $Q_4$ , and so,

$a r c sin \in Q_{4}$ $arc sin in Q_4$ is also negative.

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How do you find the exact value of $sin ({tan}^{- 1} - \frac{5}{7})$ $sin(tan^-1 -5/7)$ ?

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How do you find the exact value of $sin ({tan}^{- 1} - \frac{5}{7})$ $sin(tan^-1 -5/7)$ ?