Identify the amplitude and period of the following functions.

Question

$q\left(x\right)=3.6\cos\left(\frac{\pi x}{24}\right)$

Accepted Answer

Welcome back, everyone. In this problem, we want to find the amplitude and the period for the trigonometric expression. P of X equals 6.4 multiplied by the cosine of pi multiplied by x divided by 15. For our answer choices, a says the amplitude is 6.4 and the period is 30. B says the amplitude is 6.4 and the period is a 15th of pi. C says the amplitude is 6.4 and the period is a 30th of pi. And d says the amplitude is 6.4 and the period is 2 15ths of pi. Now, what do we know here? Well, we're trying to find the amplitude and the period for our expression and we know that this is a trigonometric expression. Recall that for a trigonometric function, they're generally written in the form a multiplied by the trigonometric function. In this case, the cosine of b x minus c plus d. Where our amplitude, okay, where the amplitude of our function equals a, that is the coefficient of the trigonometric term. And the period equals 2 pi divided by b, where b is the coefficient of the X term. So if we can figure out the values of a and b from p of x, then we'll be able to find the amplitude and the period. Now, a, which is the coefficient of the trigonometric function, in this case, would be 6.4 and b, which is the coefficient of the x term, notice that our x term is let me write it down here. Our x term is pi multiplied by x divided by 15. And we can rewrite that as pi divided by 15 multiplied by x which tells us then that b must be equal to a 15th of pi. So since we have our values for A and B, we should be able to find the amplitude and the period right away. We know that our amplitude equals a, which is 6.4. Next, our period would be equal to 2 pi divided by b. So in this case, it would be 2 pi divided by a 15th of pi, which we can rewrite as 2 pi multiplied by 15 divided by pi. Since pi is a common factor, we can cancel the those out and that leaves us with 2 multiplied by 15, which is 30. Therefore, for our function, the amplitude is 6.4 and the period is 30, which in our answer choices, that would have been answer choice a. Thanks a lot for watching everyone. I hope this video helped.

Identify the amplitude and period of the following functions.﻿q(x)=3.6cos⁡(πx24)q\left(x\right)=3.6\cos\left(\frac{\pi x}{24}\right)q(x)=3.6cos(24πx​)﻿

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Identify the amplitude and period of the following functions.
$q\left(x\right)=3.6\cos\left(\frac{\pi x}{24}\right)$