What is the general solution for sin(x)=-3/4 ,pi<x<(3pi)/4 ?

The general solution for sin(x)=-3/4 ,pi<x<(3pi)/4 is No Solution for x\in\mathbb{R}

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sin(x)=-3/4 ,pi<x<(3pi)/4

sin (x) = - \frac{3}{4}, π < x < \frac{3 π}{4}

No Solution for x \in R

Solution steps

sin (x) = - \frac{3}{4}, π < x < \frac{3 π}{4}

Apply trig inverse properties

x = arcsin (- \frac{3}{4}) + 2 πn, x = π + arcsin (\frac{3}{4}) + 2 πn

Solutions for the range

π < x < \frac{3 π}{4}

No Solution for x \in R

cos (2 x) + cos (x) = 0, 0 \leq x < 2 π

10 cos^{2} (x) = 5

cos (θ) = \frac{5}{9}

sin^{2} (x) = 5 (cos (x) + 1)

tan (2 x - \frac{π}{6}) = - \frac{1}{3}

What is the general solution for sin(x)=-3/4 ,pi<x<(3pi)/4 ?
The general solution for sin(x)=-3/4 ,pi<x<(3pi)/4 is No Solution for x\in\mathbb{R}