What is the general solution for sin(θ)= 8/10 ?

The general solution for sin(θ)= 8/10 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin

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sin(θ)= 8/10

sin (θ) = \frac{8}{10}

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

Degrees

θ = 53.13010 \dots^{\circ} + 36 0^{\circ} n, θ = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{8}{10}

Cancel the common factor:

2

sin (θ) = \frac{4}{5}

Apply trig inverse properties

sin (θ) = \frac{4}{5}

General solutions for

sin (θ) = \frac{4}{5}

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

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

- 10 = 8 tan (x) + 6

- 4 sin (2 θ) = 5 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

2 cos (2 x) + cos (x) - 1 = 0

0.79 = sin (x)

1 + cot (x) = csc (x)

What is the general solution for sin(θ)= 8/10 ?
The general solution for sin(θ)= 8/10 is θ=0.92729…+2pin,θ=pi-0.92729…+2pin