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

d) -1

step-by-step explanation:

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !