Question

Find the exact value of tan (arcsin (2/5))

Answer 1

\(\bf tan\left(sin^{-1}\left(\frac{2}{5}\right)\right)\\ \quad \\ \quad \\
sin(\theta)=\cfrac{2}{5}\implies \cfrac{opposite}{hypotenuse}\implies \cfrac{b}{c}\\ \quad \\
\textit{due to constraints on the inverse function }\quad b= 2\\
\textit{means is in the 1st Quadrant, cosine is also positive there}\\ \quad \\
c^2 = a^2+b^2\implies \sqrt{c^2-b^2} = a\\ \quad \\
\textit{keep in mind that}\qquad cos(\theta) = \cfrac{a}{c}\)

Answer 2

why do we need the cosine of the angle? well
we already know what the sine is, if we get cosine, then \(\bf tan(\theta) = \cfrac{sin(\theta)}{cos(\theta)}\implies \cfrac{\frac{2}{5}}{\frac{a}{c}}
\)

Answer 3

Is that the exact value of tan ? @jdoe0001

Answer 4

get cosine, and then you can get tangent

Answer 5

Cos = 4.6 / 5 ? @jdoe0001