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Chapter 6: Q. 13 (page 437)

Find a sinusoidal function for the following graph.

Short Answer

Expert verified

The sinusoidal function for given graph is : $y = 3 \cos (\frac{x}{2}) o r 3 \sin (\frac{π}{2} - \frac{x}{2})$

Step by step solution

01

Step 1. Given information

02

Step 2. Assume the graph equation

This shown graph shows the characteristics of the cosine function, it is symmetric about the y-axis

so let's assume the graph like

y = A \cos (ω x)

from figure

amplitude $|A| = 3$

period $T = 12$

03

Step 3. calculating the ω

We know that $T = \frac{2 π}{ω}$

$12 = \frac{2 π}{ω} ω = \frac{π}{6}$

so,the cosine function is,for amplitude 3 and $ω = \frac{π}{6}$ is

$y = 3 \cos (\frac{π}{6} x) o r 3 \sin (\frac{π}{2} - \frac{π}{6} x)$

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Most popular questions from this chapter

If the radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$ , then the measure of the angle is $1_______$ .

Find the exact value of each expression. Do not use a calculator.

$2 \sin \frac{π}{4} + 3 \tan \frac{π}{4}$

Convert each angle in degrees to radians. Express your answer as a multiple of $π$ .

$270 °$

Convert each angle in degree to radians. express your answer as a multiple of $π$ .

$- 225 °$

Convert angle in radian to degree-

$\frac{5 π}{6}$

See all solutions

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