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Anna71 [15]
3 years ago
5

Find all values of x in the interval [0, 2π] that satisfy the equation. 6sin²(x) = 3

Mathematics
1 answer:
34kurt3 years ago
5 0

Answer:

The solutions are π/4, 3π/4,5π/4,7π/4

Step-by-step explanation:

The given equation is

6sin²(x) = 3

Divide by 6 to get:

{ \sin}^{2} (x) =  \frac{1}{2}

This implies that;

\sin(x) = \pm  \frac{ \sqrt{2} }{2}

If

\sin(x) = \frac{ \sqrt{2} }{2}

x =  \frac{\pi}{4}

in the first quadrant

x =  \frac{3\pi}{4}

in the second quadrant.

If

\sin(x) = -  \frac{ \sqrt{2} }{2}

x =  \frac{5\pi}{4}

in the third quadrant

x =  \frac{7\pi}{4}

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