9514 1404 393
Answer:
x ∈ {{0.30773985, 1.26305647, 1.87853618, 2.83385280, 3.44933251, 4.40464913, 5.02012883, 5.97544545}
Step-by-step explanation:
Divide by the coefficient of the sine function, take the root, then use the arcsine function to find the angles.
[tex]3\sin^2(2x)=1\\\\\sin^2(2x)=\dfrac{1}{3}\\\\ \sin(2x)=\pm\sqrt{\dfrac{1}{3}}\\\\2x=\pm\arcsin\left(\dfrac{\sqrt{3}}{3}\right)+n\pi\\\\x=\dfrac{\pm\arcsin\left(\dfrac{\sqrt{3}}{3}\right)+n\pi}{2}[/tex]
The numerical values are approximately ...
x ∈ {{0.30773985, 1.26305647, 1.87853618, 2.83385280, 3.44933251, 4.40464913, 5.02012883, 5.97544545}
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The graph shows the zeros of 3sin²(2x) -1.
