What is the general solution for sin(θ)= 7/10 ?

The general solution for sin(θ)= 7/10 is θ=0.77539…+2pin,θ=pi-0.77539…+2pin

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sin(θ)= 7/10

sin (θ) = \frac{7}{10}

θ = 0.77539 \dots + 2 πn, θ = π - 0.77539 \dots + 2 πn

Degrees

θ = 44.42700 \dots^{\circ} + 36 0^{\circ} n, θ = 135.57299 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{7}{10}

Apply trig inverse properties

sin (θ) = \frac{7}{10}

General solutions for

sin (θ) = \frac{7}{10}

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

θ = arcsin (\frac{7}{10}) + 2 πn, θ = π - arcsin (\frac{7}{10}) + 2 πn

θ = arcsin (\frac{7}{10}) + 2 πn, θ = π - arcsin (\frac{7}{10}) + 2 πn

Show solutions in decimal form

θ = 0.77539 \dots + 2 πn, θ = π - 0.77539 \dots + 2 πn

tan (5 x) = 1

sec (5 x) = 2

5 sin (θ) - 1 = 3 sin (θ)

2 cos^{2} (w) - cos (w) - 1 = 0

3 csc (θ) - 3 = 0

What is the general solution for sin(θ)= 7/10 ?
The general solution for sin(θ)= 7/10 is θ=0.77539…+2pin,θ=pi-0.77539…+2pin