Chapter 14: Q12. (page 767)

Find the amplitude if it exists and period of the function $y = \frac{3}{4} \cos (\frac{θ}{2})$ and then graph the function.

Short Answer

Expert verified

The amplitude of $y = \frac{3}{4} \cos (\frac{θ}{2})$ is $\frac{3}{4}$ .

The period of $y = \frac{3}{4} \cos (\frac{θ}{2})$ is $4 π$ .

Step by step solution

Step 1. Write down the given information.

The given function is $y = \frac{3}{4} \cos (\frac{θ}{2})$ .

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 amplitude and period of the given function.

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

The amplitude of $y = \frac{3}{4} \cos (\frac{θ}{2})$ is $|\frac{3}{4}| = \frac{3}{4}$ .

The period of $y = \frac{3}{4} \cos (\frac{θ}{2})$ is $\frac{2 π}{|\frac{1}{2}|} = 4 π$ .

Step 4. Sketch the graph for the function.

The graph for the function $y = \frac{3}{4} \cos (\frac{θ}{2})$ is shown below.

Step 5. Conclusion.

The amplitude of $y = 4 \cos (\frac{3 θ}{4})$ is $\frac{3}{4}$ .

The period of $y = \frac{3}{4} \cos (\frac{θ}{2})$ is $4 π$ .

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Find the amplitude if it exists and period of the function $y = \frac{3}{4} \cos (\frac{θ}{2})$ and then graph the function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Evaluating amplitude and period of the given function.

Step 4. Sketch the graph for the function.

Step 5. Conclusion.

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Find the amplitude if it exists and period of the function y=34cosθ2 and then graph the function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Evaluating amplitude and period of the given function.

Step 4. Sketch the graph for the function.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Find the amplitude if it exists and period of the function $y = \frac{3}{4} \cos (\frac{θ}{2})$ and then graph the function.