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

The general solution for sin(x)=-3/4 is x=-0.84806…+2pin,x=pi+0.84806…+2pin

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sin(x)=-3/4

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

x = - 0.84806 \dots + 2 πn, x = π + 0.84806 \dots + 2 πn

Degrees

x = - 48.59037 \dots^{\circ} + 36 0^{\circ} n, x = 228.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

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

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

Show solutions in decimal form

x = - 0.84806 \dots + 2 πn, x = π + 0.84806 \dots + 2 πn

sin (2 x - \frac{π}{3}) = \frac{1}{2}

23 sin (2Θ) = 3, 0 \leq Θ \leq 2 π

4 cos^{2} (x) = 5 + 4 sin (x)

2 sin^{2} (x) + 3 sin (x) = 0

cos^{2} (x) - sin (x) = 1

What is the general solution for sin(x)=-3/4 ?
The general solution for sin(x)=-3/4 is x=-0.84806…+2pin,x=pi+0.84806…+2pin