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 bx 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 two pi divided by b. Using this, you can solve for b by simply setting two pi over b equal to the period that you're given. So we're going to have that 20 pi is equal to two pi 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 going to rewrite this actually as 20 pi times b, and that's going to be equal to two pi. Now from here, what I can actually do is divide both sides of the equation by 20 pi. This will get the 20 pis to cancel on the left side of this equation, leaving me with just b. And we'll have that b is equal to two 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 two over 20. And two over 20 reduces to one over 10, because 20 is the same thing as two times 10, and then if you cancel the twos, you'll just have one 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

12. Trigonometric Functions

Graphs of Sine & Cosine

Business Calculus

12. Trigonometric Functions

Graphs of Sine & Cosine

Struggling with Business Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

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

The period of a cosine function is given by the formula T = \frac{2\pi}{b}, where b is the coefficient of x in the argument of the cosine function.

We are given that the period T = 20\pi. Substitute this value into the formula: 20\pi = \frac{2\pi}{b}.

To isolate b, multiply both sides of the equation by b: b \cdot 20\pi = 2\pi.

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

Simplify the fraction by canceling \pi and reducing: b = \frac{1}{10}.

5:53m

Watch next

Master Graph of Sine and Cosine Function with a bite sized video explanation from Patrick

Start learning

Graphs of Sine & Cosine practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice