Find the exact value of the expression. $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$
A) $3 / 5$
B) $5 / 3$
C) $- 3 / 5$
D) $- 5 / 3$
E)none of these

Question

Quizplus · Accepted Answer

To find the exact value of $\tan(\sin^{-1}(\frac{3}{5}))$, we consider a right triangle where the opposite side is 3, the hypotenuse is 5, and we need to find the adjacent side. Using the Pythagorean theorem, the adjacent side is $\sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$. Therefore, $\tan(\sin^{-1}(\frac{3}{5})) = \frac{opposite}{adjacent} = \frac{3}{4}$, which is not listed among the options.

Find the Exact Value of the Expression tan⁡(sin⁡−135)\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)tan(sin−153​)

Find the Exact Value of the Expression $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$