# Math III

For a particular angle theta, the cosine function f(x) = a cos b(theta) has the following values within one cycle of the function: f(0)=4;f(pi/4)=0;f(pi/2)=-4;f(3pi/4)=0;f(pi)=4. What is the rule for the cosine function?
a. y=2cos4theta
b. y=4cos2theta
c. y=-4cos3theta
d. y=1/4cos2theta

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1. huh? Just work with the numbers:
a cos b(theta)
has the following values within one cycle of the function: f(0)=4;f(pi/4)=0;f(pi/2)=-4;f(3pi/4)=0;f(pi)=4

acos(b*0) = 4
so, a=4

4cos(b*pi/2) = -4,
so, b*pi/2 = pi
b = 2

f(θ) = 4cos(2θ)

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2. Thanks steve!

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