Question

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) = 2, f(pi/4) = 0, f(pi/2) = -2, f(3pi/4) = 0, f(pi) = 2

what is the rule for the cosine function???

Answer 1

f(x) = 2 cos 2θ

Explanation:

Equation is f(x) = a cos bθ

We have f(0) = 2

a cos (b x 0) = 2

a = 2

So f(x) = 2 cos bθ

We also have
`f((\pi)/(4) )=0`

`2cos(b* (\pi )/(4))=0\\ \\b* (\pi )/(4)=(\pi )/(2)\\\\b=2`

So the equation is f(x) = 2 cos 2θ

Answer 2

`y=a cos(b\theta)`


`f(0)=2 \\2=a cos((b * 0)) \\2=a cos(0) \\2=a * 1 \\a=2 \\ \\f( (\pi)/(4) )=0 \\0=a \cos{(b * (\pi)/(4))} \\\cos{ (b\pi)/(4)}=0 \\(b\pi)/(4)=(\pi)/(2) \\b= 2 \\ \\y=2 cos( 2\theta)`