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Chapter 6: Q. 65 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

$y = - 3 \cos (\frac{1}{2} x)$

Step by step solution

01

Step 1. Inspecting the y-intercept

Referring to the given graph the type of sinusoid can be determined immediately by inspecting its y- intercept if its at a maximum(highest point) and a minimum(lowest point) or neither

Since the minimum is at its y-intercept, then the graph is a cosine function and hence, $A < 0$ .

02

Step 2. Find the amplitude and period

From the graph, $y_{m i n} = - 3 y_{m a x} = 3$

$A = \frac{1}{2} (y_{m a x} - y_{m i n}) A = \frac{1}{2} (3 - (- 3)) A = \frac{1}{2} (6) A = 3$

Using the maximum at $x = 0$ , the next maximum occurs at $x = 4 π$

Therefore,

$T = 4 π$

03

Step 3. Solve for the equation

$ω = \frac{2 π}{T} ω = \frac{2 π}{4 π} ω = \frac{1}{2}$

Therefore, the equation of the graph is

$y = - 3 \cos (\frac{1}{2} x)$

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Most popular questions from this chapter

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

$- 60 °$

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$390 °$

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

Explain the difference between linear speed and angular speed.

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\sin \frac{π}{8}$

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