Question

Find the exact value of tan (arcsin (2/5)). For full credit, explain your reasoning.
I have no idea what steps to take to solve this. Help please!

Answer 1

ok whenever you have something in the form:
\[trig_1(trig_2^{-1}(x))\]
you could do the following:
1st) Let \[u=trig_2^{-1}(x)\]
2nd) \[trig_2(u)=x \text{ just rewriting first step } \]
3rd) Draw a right triangle for the equation in the 2nd step and find all side measurements.
4th) Find \[trig_1(u)\]
4th step will be your answer

Answer 2

trig_1 and trig_2 are just a trig function like cos sin tan csc sec or cot