Expert: Bobby Soltani - 3/18/2005

Question
1) find an angle (theta), 0 <= theta <= 2pi, such that the sum of the squares of the sine and cosine of theta is equal to twice the product of the sine and cosine of theta.

Answer
Hi Amy,

Writing the problem in equation form, where theta is x, we have:

(sin x)^2 + (cos x)^2 = 2 * (sin x)*(cos x)

from the properties of sin and cos, we know that the left hand side is equal to 1.

1 = 2*(sin x)*(cos x)
divide both sides by 2

(1/2) = (sin x)(cos x)

From looking at a sin/cos table, we can see that sin and cos of pi/4 is SQRT(2)/2.  This value solves the equation.

(1/2) = (SQRT(2)/2)*((SQRT(2)/2) = 2/4 = 1/2

Let me know if you have any questions.

Bobby