Use the trigonometric substitution to write the algebraic eq

Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of , where /2 < < /2.

5 =sqrt( 25 x^2) , x = 5 sin

Find sin(theta), cos(theta).

5 = sqrt ( 25 - x^2 )

x = 5 sin theta

substituting the value of x

5 = sqrt ( 25 - ( 5 sin theta )^2)

5 = sqrt ( 25 - 25 sin^2 theta )

5 = sqrt ( 25 ( 1 - sin^2 theta ))

1 - sin^2 theta = cos^2 theta

5 = sqrt ( 25 * cos^2 theta )

5 = + - 5 cos theta

cos theta = + - 1

sin theta = 0