The number of solutions of sin^2 theta = frac | vedclass

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(C) Given the equation: $\sin^2 	heta = \frac{1}{2}$.Taking the square root on both sides,we get $\sin 	heta = \pm \frac{1}{\sqrt{2}}$.Since $	heta

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two

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(C) Given the equation: $\sin^2 	heta = \frac{1}{2}$.Taking the square root on both sides,we get $\sin 	heta = \pm \frac{1}{\sqrt{2}}$.Since $	heta \in [0, \pi]$,the sine function is non-negative in this interval.Therefore,$\sin 	heta = \frac{1}{\sqrt{2}}$.The values of $	heta$ in $[0, \pi]$ that satisfy $\sin 	heta = \frac{1}{\sqrt{2}}$ are $	heta = \frac{\pi}{4}$ and $	heta = \frac{3\pi}{4}$.Thus,there are $2$ solutions.

The number of solutions of $\sin^2 \theta = \frac{1}{2}$ in the interval $[0, \pi]$ is . . . . . .

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