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Chapter 6: Q. 69 (page 411)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

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

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

At its y-intercept neither maximum or nor minimum, then the graph is a sine function and the minimum occurs before the maximum hence,

$A < 0$

02

Step 2. Find the amplitude and period

From the graph, $y_{m i n} = - 1 y_{m a x} = 1$

role="math" localid="1646377759931" $A = - \frac{1}{2} (y_{m a x} - y_{m i n}) A = - \frac{1}{2} (1 - (- 1)) A = - \frac{1}{2} (2) A = - 1 |A| = 1$

Using the maximum at $\frac{π}{3}$ , the next maximum occurs at $\frac{5 π}{3}$

Therefore,

$T = \frac{4 π}{3}$

03

Step 3. Solve for the equation

$ω = \frac{2 π}{T} ω = \frac{2 π \times 3}{4 π} ω = \frac{3}{2}$

Therefore, the equation of the graph is

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

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Most popular questions from this chapter

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

$\sin 28 °$

Nautical Miles A nautical mile equals the length of arc subtended by a central angle of 1 minute on a great circle† on the surface of Earth. See the figure. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\cot (\frac{π}{12})$

Pulleys Two pulleys, one with radius $r_{1}$ and the other with radius $r_{2}$ , are connected by a belt. The pulley with radius $r_{1}$ rotates at $v_{1}$ revolutions per minute, whereas the pulley with

radius $r_{2}$ rotates at $v_{2}$ revolutions per minute. Show thatrole="math" localid="1646296862603" $\frac{r_{1}}{r_{2}} = \frac{ω_{1}}{ω_{2}}$

In Problems $4 - 6$ convert each angle in radians to degrees.

$5 . \frac{9 π}{2}$

See all solutions

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