Question

Cos(sin^-1 x) = 1/2 find the value of x

Answer 1

Step-by-step explanation:

Let θ = Sin-1x, then sinθ = x = x/1 = opposite / hypotenuse

Draw a right triangle in the first quadrant with the vertex of θ at the origin, vertical side of length x, and hypotenuse of

length 1. By the Pythagorean Theorem, the horizontal side (along the x-axis) has length √(1-x2).

So, cos(Sin-1x) = cosθ = adjacent/hypotenuse = √(1-x2) / 1 = √(1-x2).

Then set the square root of 1 minus x squared equal to one half and solve for x.