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

$y=a \cos{b\theta}$

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

Answer 2

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