1. derive formulas for the following:
a. sin(2theta)
b. cos(2theta)

Sin(2theta)= 2sintheta costheta

Cos(2theta) = 2cos²theta - 1

Cos(2theta) = 1 - 2sin²theta

Step-by-step explanation:

Sin(2theta) = Sin(theta+theta)

Sin(theta+theta)= sintheta costheta + costheta sintheta

Since costheta and sintheta are occurring twice in the addition

Sin(theta+theta)= 2sintheta costheta

Cos(2theta) = cos(theta+theta)

= costheta costheta - sintheta sintheta

= cos²theta - sin²theta ... 1

From sin²theta + cos²theta = 1

Sin²theta = 1 - cos²theta ... 2

Substituting 2 into 1

Cos(2theta) = cos²theta - (1 - cos²theta)

Cos (2theta) = cos²theta - 1 + cos²theta

Cos(2theta) = 2cos²theta - 1

Cos(2theta) = 1 - 2sin²theta

a 360 degree rotation

step-by-step explanation:

4.28095238095 that is the answer