Question

How to rewrite sin(arccos(x)) without trig function?

a) √(1-x²)
b) 1/√(1-x²)
c) √(x²-1)
d) 1/√(x²-1)

Answer 1

To rewrite sin(arccos(x)) without trigonometric functions, we can use the identity sin²θ + cos²θ = 1. By substituting cos(θ) with x, we get the correct answer as option a) √(1-x²).

Step-by-step explanation:

To rewrite sin(arccos(x)) without trigonometric functions, we can use the identity sin²θ + cos²θ = 1. Let's assume arccos(x) = θ.

cos(θ) = x. Now we can rewrite sin(θ) as sin(θ) = √(1 - cos²(θ)). Substituting cos(θ) with x, we get sin(arccos(x)) = √(1 - x²).

Therefore, option a) √(1-x²) is the correct rewrite of sin(arccos(x)) without using trigonometric functions.