Chapter 14: Q. 43PA (page 768)

What is the period of $f (x) = \frac{1}{2} \cos (3 x)$ and then graph the function.
$(A) 120 {}^{\circ}{(B)} 180 {}^{\circ}{(C)} 360 {}^{\circ}{(D)} 720 °$

Short Answer

Expert verified

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $120 °$ . So, option (A) is correct.

Step by step solution

Step 1. Write down the given information.

The given function is $f (x) = \frac{1}{2} \cos (3 x)$ .

Step 2. Concept used.

A function of the form $y = a \sin (b x) and y = a \cos (b x)$ has amplitude of $|a|$ and period $\frac{360 °}{|b|} or \frac{2 π}{|b|}$ .

Step 3. Evaluating period of the given function.

With the help of concept stated above, the period of the function is evaluated as:

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $\frac{360 °}{|3|} = 120 °$ .

Step 4. Conclusion.

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $120 °$ . So, option (A) is correct.

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What is the period of $f (x) = \frac{1}{2} \cos (3 x)$ and then graph the function.
$(A) 120 {}^{\circ}{(B)} 180 {}^{\circ}{(C)} 360 {}^{\circ}{(D)} 720 °$

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Evaluating period of the given function.

Step 4. Conclusion.

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What is the period of fx=12cos3x and then graph the function.A120B∘180C∘360D∘720°

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Evaluating period of the given function.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

What is the period of $f (x) = \frac{1}{2} \cos (3 x)$ and then graph the function.
$(A) 120 {}^{\circ}{(B)} 180 {}^{\circ}{(C)} 360 {}^{\circ}{(D)} 720 °$