What is the general solution for sin(θ)=-0.9 ?

The general solution for sin(θ)=-0.9 is θ=-1.11976…+2pin,θ=pi+1.11976…+2pin

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sin(θ)=-0.9

sin (θ) = - 0.9

θ = - 1.11976 \dots + 2 πn, θ = π + 1.11976 \dots + 2 πn

Degrees

θ = - 64.15806 \dots^{\circ} + 36 0^{\circ} n, θ = 244.15806 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - 0.9

Apply trig inverse properties

sin (θ) = - 0.9

General solutions for

sin (θ) = - 0.9

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

θ = arcsin (- 0.9) + 2 πn, θ = π + arcsin (0.9) + 2 πn

θ = arcsin (- 0.9) + 2 πn, θ = π + arcsin (0.9) + 2 πn

Show solutions in decimal form

θ = - 1.11976 \dots + 2 πn, θ = π + 1.11976 \dots + 2 πn

cos (2 T) = 1, 0 \leq T \leq 2 π

2 - 2 cos^{2} (\frac{x}{2}) = 2 cos^{2} (x)

sec^{2} (θ) - 2 = tan^{2} (θ)

cos (x) = sin (x) + 1

2 sin^{2} (θ) = 3 (1 - cos (- θ))

What is the general solution for sin(θ)=-0.9 ?
The general solution for sin(θ)=-0.9 is θ=-1.11976…+2pin,θ=pi+1.11976…+2pin