What is the general solution for 3sin(θ)+5=6 ?

The general solution for 3sin(θ)+5=6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin

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3sin(θ)+5=6

3 sin (θ) + 5 = 6

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

Solution steps

3 sin (θ) + 5 = 6

Move

5

to the right side

3 sin (θ) = 1

Divide both sides by

3

sin (θ) = \frac{1}{3}

Apply trig inverse properties

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

\frac{9}{73} + sin^{2} (θ) = 1

x, - 2 sin (2 x) - 2 sin (4 x) = 0

6.15 = 220 sin (377 t)

x, 3 sec (5 x) - 2 = 0

cos (t) + cos (2 t) = 0, sin (t) + sin (2 t) = 0

What is the general solution for 3sin(θ)+5=6 ?
The general solution for 3sin(θ)+5=6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin