Question

Find the exact value of sin (arccos (three fifths)). for full credit, explain your reasoning.

Answer 1

We want to evaluate sin(cos⁻¹(3/5)).

Note that
sin²x + cos²x = 1
Therefore
sin²x = 1 - cos²x

Let y = cos⁻¹(3/5)
Then
cos(y) = 3/5
sin²y = 1 - cos²y = 1 - 9/25 = 16/25
sin(y) = 4/5

Therefore
sin(cos⁻¹(3/5)) = sin(y) = 4/5

Answer: 4/5