Simplify the expression
√81−y ^2 as much as possible after substituting
9 sin x for y.
First, substitute 9 sin x for y:
√81−y ^2 = √81−(9 sin x)^2
Simplify the expression inside the square root:
√81−(9 sin x)^2 = √81−81sin^2x
Simplify further, using the identity cos^2x + sin^2x = 1:
√81−81sin^2x = √81(1-sin^2x) = √(9^2)(cos^2x)
Simplify using the fact that the square root of a square is the absolute value of the expression inside:
√(9^2)(cos^2x) = |9cosx|
Therefore, √81−y ^2 simplifies to |9cosx| after substituting 9 sin x for y.