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Find all solutions of the equation in the interval [0, 2pi).
2 sin 0-sqrt2 = 0
Write your answer in radians in terms of n.
If there is more than one solution, separate them with commas.

Find all solutions of the equation in the interval [0, 2pi). 2 sin 0-sqrt2 = 0 Write your answer in radians in terms of n. If there is more than one solution, s class=

Answer :

xKelvin

Answer:

[tex]\displaystyle \theta=\frac{\pi}{4}, \frac{3\pi}{4}[/tex]

Step-by-step explanation:

We want to find the solutions to:

[tex]2\sin(\theta)-\sqrt{2}=0[/tex]

Within the interval [0, 2π).

First, isolate the sine:

[tex]\displaystyle \sin(\theta)=\frac{\sqrt{2}}{2}[/tex]

Recall the unit circle. This is true twice: at π/4 and 3π/4.

Hence, our solutions are:

[tex]\displaystyle \theta=\frac{\pi}{4}, \frac{3\pi}{4}[/tex]

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