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Q: What is cosine squared theta equal to'?

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It is 1.

To determine what negative sine squared plus cosine squared is equal to, start with the primary trigonometric identity, which is based on the pythagorean theorem...sin2(theta) + cos2(theta) = 1... and then solve for the question...cos2(theta) = 1 - sin2(theta)2 cos2(theta) = 1 - sin2(theta) + cos2(theta)2 cos2(theta) - 1 = - sin2(theta) + cos2(theta)

There is no easy simplification.

No, they do not.

If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432

It is 2*sin(theta)*sin(theta) because that is how multiplication is defined!

It is a non-linear function of theta.

Since secant theta is the same as 1 / cosine theta, the answer is any values for which cosine theta is zero, for example, pi/2.

No, not necessarily. Cosine theta is equal to 1 only when theta is equal to zero and multiples of 2 pi radians or multiples of 360 degrees. This is because cosine theta is hypotenuse over adjacent, and the ratio 1 only occurs at 0, 360, 720, etc. or 0, 2 pi, 4 pi, etc.

cosine (90- theta) = sine (theta)

Tan^2

You could just pull out the half: it will be (1/2) cos squared x.

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