The Period for the function y=cos(bx)y=\cos\left(bx\right)y=cos(bx) is T=20πT=20\piT=20π. Determine the correct value of b.

b = 1 10 b=\frac{1}{10} b = 10 1

The Period for the function y = cos ( b x ) y=\cos\left(bx\right) y = cos ( b x ) is T = 20 π T=20\pi T = 20 π . Determine the correct value of b.

Hey, everyone. Let's give this problem a try. So here we're told the period of the function y equals the cosine of b x is 20 pi. Determine the correct value for b. Now to solve this problem, all you really have to do is remember that the period for a sine or cosine function is 2 pi divided by b. Using this, you can solve for b by simply setting 2pi over b equal to the period that you're given. So So we're going to have that 20pi is equal to 2pi over b, and now we just need to solve for b. Now my first step is going to be to multiply b on both sides of this equation, and that'll get the b's to cancel on the right side. Giving us b times 20 pi is equal, and I'm gonna rewrite this actually as 20 pi times b, and that's going to be equal to 2pi. Now from here, what I can actually do is divide both sides of the equation by 20pi. This will get the 20 pis to cancel on the left side of this equation, leaving me with just b. And I'll have that b is equal to 2 pi divided by 20 pi. Now what I notice here is that the pi's are going to cancel each other, and then we have 2 over 20, and 2 over 20 reduces to 1 over 10, because 20 is the same thing as 2 times 10, and then if you cancel the twos, you'll just have 1 over 10. So this is our solution for b and the answer to this problem.

The Period for the function y = cos ⁡ ( b x ) y=\cos\left(bx\right) y = cos ( b x ) is T = 20 π T=20\pi T = 20 π . Determine the correct value of b.

b = 1 10 b=\frac{1}{10} b = 10 1

b = 1 20 b=\frac{1}{20} b = 20 1

10. Graphing Trigonometric Functions

Graphs of the Sine and Cosine Functions

Precalculus

10. Graphing Trigonometric Functions

Graphs of the Sine and Cosine Functions

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Multiple Choice

The Period for the function $y=\cos\left(bx\right)$ is $T=20\pi$ . Determine the correct value of b.

$b=\frac{1}{10}$

$b=10$

$b=20$

$b=\frac{1}{20}$

Verified step by step guidance

Understand that the period of a cosine function y = cos(bx) is given by the formula T = \frac{2\pi}{b}.

Set the given period T = 20\pi equal to the formula for the period: \frac{2\pi}{b} = 20\pi.

To solve for b, first isolate b by multiplying both sides of the equation by b: 2\pi = 20\pi \cdot b.

Divide both sides of the equation by 20\pi to solve for b: b = \frac{2\pi}{20\pi}.

Simplify the expression \frac{2\pi}{20\pi} by canceling \pi from the numerator and the denominator, resulting in b = \frac{1}{10}.

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