recall that the function theta fb arcsinb is a partial inv

recall that the function theta = f(b) = arcsin(b) is a partial inverse for the function b=sin(theta). Find the equivalent algebraic formula for the expression tan(arcsin(3t/2))

Solution

tan(arc sin(3t/2))

Let arc sin(3t/2) = c

Therrfore sin c= 3t/2

Here opposite=3t

Hypotenuse=2

Therefore adjacent=sqrt(2² - (3t)²)

adjacent= sqrt(4-9t²)

Tan t=opposite/adjacent = 3t/sqrt(4 -9t²)

Hence tan(arc sin(3t/2)) = 3t/(sqrt(4-9t²))