What is the general solution for sin(θ)=(sqrt(5))/4 ?

The general solution for sin(θ)=(sqrt(5))/4 is θ=0.59319…+2pin,θ=pi-0.59319…+2pin

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sin(θ)=(sqrt(5))/4

sin (θ) = \frac{5}{4}

θ = 0.59319 \dots + 2 πn, θ = π - 0.59319 \dots + 2 πn

Degrees

θ = 33.98784 \dots^{\circ} + 36 0^{\circ} n, θ = 146.01215 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{5}{4}

Apply trig inverse properties

sin (θ) = \frac{5}{4}

General solutions for

sin (θ) = \frac{5}{4}

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

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

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

Show solutions in decimal form

θ = 0.59319 \dots + 2 πn, θ = π - 0.59319 \dots + 2 πn

100 = 5040 cos (θ)

cos (3 x) = \frac{2}{3}

cos (x) (csc (x) + 2) = 0

arctan (θ) = \frac{π}{4}

4 cos^{3} (x) - 7 cos (x) - 3 = 0

What is the general solution for sin(θ)=(sqrt(5))/4 ?
The general solution for sin(θ)=(sqrt(5))/4 is θ=0.59319…+2pin,θ=pi-0.59319…+2pin