What is the general solution for sin(x)=-0.61 ?

The general solution for sin(x)=-0.61 is x=-0.65606…+2pin,x=pi+0.65606…+2pin

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sin(x)=-0.61

sin (x) = - 0.61

x = - 0.65606 \dots + 2 πn, x = π + 0.65606 \dots + 2 πn

Degrees

x = - 37.58950 \dots^{\circ} + 36 0^{\circ} n, x = 217.58950 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - 0.61

Apply trig inverse properties

sin (x) = - 0.61

General solutions for

sin (x) = - 0.61

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

x = arcsin (- 0.61) + 2 πn, x = π + arcsin (0.61) + 2 πn

x = arcsin (- 0.61) + 2 πn, x = π + arcsin (0.61) + 2 πn

Show solutions in decimal form

x = - 0.65606 \dots + 2 πn, x = π + 0.65606 \dots + 2 πn

2 cos (3 x) + 2 = 0

cos (2 x) - sin (- x) = 0

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

sin (θ) - 2 sin (θ) cos (θ) = 0

6 cos^{2} (x) + cos (2 x) = 1

What is the general solution for sin(x)=-0.61 ?
The general solution for sin(x)=-0.61 is x=-0.65606…+2pin,x=pi+0.65606…+2pin