Question

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume 0 ≤ θ <π/2 √(9-x²), x=3 sinθ

Answer 1

To make the trigonometric substitution, substitute x = 3sinθ into the given expression √(9-x²) and simplify to √(9-9sin²θ).

Step-by-step explanation:

To make the trigonometric substitution, we substitute x = 3sinθ into the given expression √(9-x²).

So, substituting x = 3sinθ gives us: √(9-(3sinθ)²).

Simplifying further, we have: √(9-9sin²θ).

The trigonometric substitution x = 3sinθ simplifies the expression to √(9-9sin²θ).