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MATH / Below is the graph of y = a csc bx for some positive constants a and b. Find b. [asy]import TrigMacros; size(500); real g(real x) return 2*csc(x/3); draw(graph(g,-6*pi + 0.01, -3*p…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Below is the graph of $y = a \csc bx$ for some positive constants aa and b.b. Find b.b. [asy]import TrigMacros; size(500); real g(real x) { return 2*csc(x/3); } draw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red); draw(graph(g,-3*pi + 0.01,-0.01),red); draw(graph(g,0.01,3*pi - 0.01),red); draw(graph(g,3*pi + 0.01,6*pi - 0.01),red); limits((-6*pi,-5),(6*pi,5),Crop); draw((-3*pi,-5)--(-3*pi,5),dashed); draw((3*pi,-5)--(3*pi,5),dashed); trig_axes(-6*pi,6*pi,-5,5,pi/2,1); layer(); rm_trig_labels(-11, 11, 2); label("11", (0,1), E); label("22", (0,2), E); label("33", (0,3), E); label("44", (0,4), E); label("−1-1", (0,-1), E); label("−2-2", (0,-2), E); label("−3-3", (0,-3), E); label("−4-4", (0,-4), E); [/asy]
Plain-text mathematical notation (without MathML)
Below is the graph of $y = a \csc bx$ for some positive constants a and b.  Find b.

[asy]import TrigMacros;

size(500);

real g(real x)
{
	return 2*csc(x/3);
}

draw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red);
draw(graph(g,-3*pi + 0.01,-0.01),red);
draw(graph(g,0.01,3*pi - 0.01),red);
draw(graph(g,3*pi + 0.01,6*pi - 0.01),red);
limits((-6*pi,-5),(6*pi,5),Crop);
draw((-3*pi,-5)--(-3*pi,5),dashed);
draw((3*pi,-5)--(3*pi,5),dashed);
trig_axes(-6*pi,6*pi,-5,5,pi/2,1);
layer();
rm_trig_labels(-11, 11, 2);

label("1", (0,1), E);
label("2", (0,2), E);
label("3", (0,3), E);
label("4", (0,4), E);
label("−1", (0,-1), E);
label("−2", (0,-2), E);
label("−3", (0,-3), E);
label("−4", (0,-4), E);
[/asy]
Original LaTeX notation
Below is the graph of $y = a \csc bx$ for some positive constants $a$ and $b.$  Find $b.$

[asy]import TrigMacros;

size(500);

real g(real x)
{
	return 2*csc(x/3);
}

draw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red);
draw(graph(g,-3*pi + 0.01,-0.01),red);
draw(graph(g,0.01,3*pi - 0.01),red);
draw(graph(g,3*pi + 0.01,6*pi - 0.01),red);
limits((-6*pi,-5),(6*pi,5),Crop);
draw((-3*pi,-5)--(-3*pi,5),dashed);
draw((3*pi,-5)--(3*pi,5),dashed);
trig_axes(-6*pi,6*pi,-5,5,pi/2,1);
layer();
rm_trig_labels(-11, 11, 2);

label("$1$", (0,1), E);
label("$2$", (0,2), E);
label("$3$", (0,3), E);
label("$4$", (0,4), E);
label("$-1$", (0,-1), E);
label("$-2$", (0,-2), E);
label("$-3$", (0,-3), E);
label("$-4$", (0,-4), E);
[/asy]

level

Level 2

type

Precalculus

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Source and history

task_id
20e184bb-ef63-51f9-8697-e04ccf197c77
task_key
precalculus--test--20e184bb-ef63-51f9-8697-e04ccf197c77
task_revision_id
1
config / split
precalculus / test

Official source

initial import