What is the general solution for sin(θ)=0.788 ?

The general solution for sin(θ)=0.788 is θ=0.90755…+2pin,θ=pi-0.90755…+2pin

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sin(θ)=0.788

sin (θ) = 0.788

θ = 0.90755 \dots + 2 πn, θ = π - 0.90755 \dots + 2 πn

Degrees

θ = 51.99899 \dots^{\circ} + 36 0^{\circ} n, θ = 128.00100 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = 0.788

Apply trig inverse properties

sin (θ) = 0.788

General solutions for

sin (θ) = 0.788

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

θ = arcsin (0.788) + 2 πn, θ = π - arcsin (0.788) + 2 πn

θ = arcsin (0.788) + 2 πn, θ = π - arcsin (0.788) + 2 πn

Show solutions in decimal form

θ = 0.90755 \dots + 2 πn, θ = π - 0.90755 \dots + 2 πn

arctan (θ) = - 3

cos (θ) = \frac{2}{6}

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

\frac{tan ( x ) ( - tan ^{2} ( x ) + 3 )}{1 - tan ^{2} ( x )} = 0

2 sin (x) - cos (x) = 0.6

What is the general solution for sin(θ)=0.788 ?
The general solution for sin(θ)=0.788 is θ=0.90755…+2pin,θ=pi-0.90755…+2pin