Question
Asked Jan 26, 2020
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Solve the equation for all solutions in the interval [0,2π).

sin(3x)=−√3/2

Express each solution in radians in exact form. Enter the solutions as a comma‑separated list.

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Expert Answer

Step 1

Find 3x using sin inverse. 

Calculus homework question answer, step 1, image 1
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Step 2

Sin is negative in 3rd and fourth quadrant. 

sin^-1(-sqrt(3)/2)= 4pi/3 and 5pi/3 in [0,2pi].

We add 2n*pi with the solutions to find the general solutions.

Calculus homework question answer, step 2, image 1
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Step 3

Find x by dividing ...

Calculus homework question answer, step 3, image 1
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