13 mark for review the function h is defined by h(θ)=a cos(bθ) for constants a and b. if h has a period of π…
13 mark for review the function h is defined by h(θ)=a cos(bθ) for constants a and b. if h has a period of π and an amplitude of 4, what are the values of a and b? a a = 2 and b = 1/2 b a = 2 and b = 2 c a = 4 and b = 1/2 d a = 4 and b = 2
Answer
Explanation:
Step1: Recall amplitude formula
The amplitude of the function $y = a\cos(b\theta)$ is $|a|$. Given amplitude is 4, so $|a|=4$, which means $a = 4$ or $a=- 4$. In the options, $a = 4$ is available.
Step2: Recall period formula
The period of the function $y=\cos(b\theta)$ is $T=\frac{2\pi}{|b|}$. Given $T = \pi$. So $\pi=\frac{2\pi}{|b|}$. Cross - multiply to get $\pi|b|=2\pi$. Divide both sides by $\pi$, we get $|b| = 2$, and since we are looking for a positive value of $b$ (common in basic trigonometric function parameterization in this context), $b = 2$.
Answer:
D. $a = 4$ and $b = 2$