What is the general solution for sin(x)=-0.23 ?

The general solution for sin(x)=-0.23 is x=-0.23207…+2pin,x=pi+0.23207…+2pin

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sin(x)=-0.23

sin (x) = - 0.23

x = - 0.23207 \dots + 2 πn, x = π + 0.23207 \dots + 2 πn

Degrees

x = - 13.29707 \dots^{\circ} + 36 0^{\circ} n, x = 193.29707 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - 0.23

Apply trig inverse properties

sin (x) = - 0.23

General solutions for

sin (x) = - 0.23

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

x = arcsin (- 0.23) + 2 πn, x = π + arcsin (0.23) + 2 πn

x = arcsin (- 0.23) + 2 πn, x = π + arcsin (0.23) + 2 πn

Show solutions in decimal form

x = - 0.23207 \dots + 2 πn, x = π + 0.23207 \dots + 2 πn

2 sin^{2} (x) + 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

cos (3 x) - 1 = sin (3 x)

sin (\frac{x}{3}) = \frac{2}{2}

2 cos (3 x) = - 3

cos (x) = cos^{2} (x)

What is the general solution for sin(x)=-0.23 ?
The general solution for sin(x)=-0.23 is x=-0.23207…+2pin,x=pi+0.23207…+2pin