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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???

Verified Answer :

\(y=a \cos{b\theta}\)

\(f(0)=2 \\2=a \cos{(b \times 0)} \\2=a \cos{0} \\2=a \times 1 \\a=2 \\ \\f( \frac{\pi}{4} )=0 \\0=a \cos{(b \times \frac{\pi}{4})} \\\cos{ \frac{b\pi}{4}}=0 \\\frac{b\pi}{4}=\frac{\pi}{2} \\b= 2 \\ \\y=2 \cos{ 2\theta}\)

Blacklash

Answer:

f(x) = 2 cos 2θ

Step-by-step 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 \(f(\frac{\pi}{4} )=0\)

      \(2cos(b\times \frac{\pi }{4})=0\\ \\b\times \frac{\pi }{4}=\frac{\pi }{2}\\\\b=2\)

So the equation is f(x) = 2 cos 2θ

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