Question

please help me find the exact value of tan (arcsin (2/5)). and explain the reasoning.

Answer 1

\(\bf tan\left[sin^{-1}\left(\frac{2}{5}\right)\right]\\ \quad \\ \quad \\
sin^{-1}\left(\frac{2}{5}\right)=\theta\qquad sin(\theta)=\cfrac{2}{5}\implies \cfrac{opposite}{hypotenuse}\implies \cfrac{b}{c}\)



use the pythagorean theorem to find "a"

once you find "a", use that to get the tangent value, recall that \(\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies \cfrac{b}{a}\)

Answer 2

For "a" i got sqrt 21...

Answer 3

thank you

Answer 4

yw