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Solve for the angle theta. (a) sin^(2)theta=3//4. (b) sin 2theta-cos theta=0.

Solve for the angle θ\theta. \newline(a) sin⁡2θ=34\sin^{2}\theta=\frac{3}{4}. \newline(b) sin⁡2θ−cos⁡θ=0\sin 2\theta-\cos \theta=0.

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Full solution

Q. Solve for the angle θ\theta. \newline(a) sin⁡2θ=34\sin^{2}\theta=\frac{3}{4}. \newline(b) sin⁡2θ−cos⁡θ=0\sin 2\theta-\cos \theta=0.
  1. Rewrite and Set Equal: Rewrite sin⁡2(θ)\sin^2(\theta) as (sin⁡(θ))2(\sin(\theta))^2 and set it equal to 34\frac{3}{4}.\newline(sin⁡(θ))2=34(\sin(\theta))^2 = \frac{3}{4}
  2. Take Square Root: Take the square root of both sides to solve for sin⁡(θ)\sin(\theta).sin⁡(θ)=±34\sin(\theta) = \pm\sqrt{\frac{3}{4}}sin⁡(θ)=±32\sin(\theta) = \pm\sqrt{\frac{3}{2}}

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