one cycle of the graph of a trigonometric function of the form y = a sin (bx) or y = a cos (bx) is given…

one cycle of the graph of a trigonometric function of the form y = a sin (bx) or y = a cos (bx) is given. determine the equation of the function represented by the following graph. the graph represents a function of the form a cos (bx) for b > 0. the period of this function is 12 (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

one cycle of the graph of a trigonometric function of the form y = a sin (bx) or y = a cos (bx) is given. determine the equation of the function represented by the following graph. the graph represents a function of the form a cos (bx) for b > 0. the period of this function is 12 (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Find the amplitude A

The amplitude is the distance from the mid - line to the maximum or minimum value of the function. The maximum value is 4 and the minimum value is - 4. So, $A = 4$.

Step2: Find the value of B

The period formula for $y = A\cos(Bx)$ is $T=\frac{2\pi}{B}$. Given that $T = 12$, we can solve for B. Rearranging the formula gives $B=\frac{2\pi}{T}$. Substituting $T = 12$ into the formula, we get $B=\frac{2\pi}{12}=\frac{\pi}{6}$.

Answer:

$y = 4\cos(\frac{\pi}{6}x)$