What is the general solution for sin(x)=-0.2 ?

The general solution for sin(x)=-0.2 is x=-0.20135…+2pin,x=pi+0.20135…+2pin

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sin(x)=-0.2

sin (x) = - 0.2

x = - 0.20135 \dots + 2 πn, x = π + 0.20135 \dots + 2 πn

Degrees

x = - 11.53695 \dots^{\circ} + 36 0^{\circ} n, x = 191.53695 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - 0.2

Apply trig inverse properties

sin (x) = - 0.2

General solutions for

sin (x) = - 0.2

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

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

Show solutions in decimal form

x = - 0.20135 \dots + 2 πn, x = π + 0.20135 \dots + 2 πn

20 cos^{2} (x) - cos (x) - 1 = 0

2 cot (x) - tan (x) + 6 = 8 - tan (x)

x, 2 sin (x) + 1 = 0

8 tan (3 x) = 8

1 = sin (θ) - cos (θ)

What is the general solution for sin(x)=-0.2 ?
The general solution for sin(x)=-0.2 is x=-0.20135…+2pin,x=pi+0.20135…+2pin