What is the general solution for sin(θ)= 9/10 ?

The general solution for sin(θ)= 9/10 is θ=1.11976…+2pin,θ=pi-1.11976…+2pin

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sin(θ)= 9/10

sin (θ) = \frac{9}{10}

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

Degrees

θ = 64.15806 \dots^{\circ} + 36 0^{\circ} n, θ = 115.84193 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{9}{10}

Apply trig inverse properties

sin (θ) = \frac{9}{10}

General solutions for

sin (θ) = \frac{9}{10}

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

θ = arcsin (\frac{9}{10}) + 2 πn, θ = π - arcsin (\frac{9}{10}) + 2 πn

θ = arcsin (\frac{9}{10}) + 2 πn, θ = π - arcsin (\frac{9}{10}) + 2 πn

Show solutions in decimal form

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

2 sec^{2} (x) - tan^{2} (x) = 3

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

4 sin (2 t) = 4 cos (t)

- 2 sin^{2} (x) + 2 cos (x) + 2 cos^{2} (x) = 0

1 + 2 sin^{2} (t) = - 5 cos (t)

What is the general solution for sin(θ)= 9/10 ?
The general solution for sin(θ)= 9/10 is θ=1.11976…+2pin,θ=pi-1.11976…+2pin