If x=3sin(theta) What is -cos(theta) in terms of x using the method of triangles Answer is -sqrt(9-x^2)?

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Triangles:
Take 3 as the hypotenuse of a right triangle,
and x opposite the angle θ -- assuming θ is acute.
Then the third side - adjacent to θ, is √(9 - x²)
So cos θ = √(9 - x²) / 3 ,
-cos θ = -√(9 - x²) / 3 ....Show more

If x = 3sinθ then,

sinθ = x/3

Now, sin²θ + cos²θ = 1

i.e. (x/3)² + cos²θ = 1

=> cos²θ = 1 - (x²/9)

=> 9cos²θ = 9 - x²

so, cos²θ = (9 - x²)/9

=> cosθ = ±√(9 - x²)/3

Hence, -cosθ = -√(9 - x²)/3

:)>...Show more