What is the general solution for sqrt(5)sin(θ+0.4636)=1 ?

The general solution for sqrt(5)sin(θ+0.4636)=1 is θ=0.46364…+2pin-0.4636,θ=pi-0.46364…+2pin-0.4636

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sqrt(5)sin(θ+0.4636)=1

5 sin (θ + 0.4636) = 1

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

Solution steps

5 sin (θ + 0.4636) = 1

Divide both sides by

5

sin (θ + 0.4636) = \frac{5}{5}

Apply trig inverse properties

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn, θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn

Solve

θ + 0.4636 = arcsin (\frac{5}{5}) + 2 πn : θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636

Solve

θ + 0.4636 = π - arcsin (\frac{5}{5}) + 2 πn : θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

θ = arcsin (\frac{1}{5}) + 2 πn - 0.4636, θ = π - arcsin (\frac{1}{5}) + 2 πn - 0.4636

Show solutions in decimal form

θ = 0.46364 \dots + 2 πn - 0.4636, θ = π - 0.46364 \dots + 2 πn - 0.4636

0 = \frac{20}{3} sin (10 t) + 5 cos (10 t)

y, arctan (y) = \frac{t ^{2}}{2}

cos (- x) = 0

2 tan^{2} (x) + 1 = 0

y, arctan (y) = \frac{x ^{3}}{3} - 2 x + c

What is the general solution for sqrt(5)sin(θ+0.4636)=1 ?
The general solution for sqrt(5)sin(θ+0.4636)=1 is θ=0.46364…+2pin-0.4636,θ=pi-0.46364…+2pin-0.4636