What is the general solution for 4sin(θ)+1=0 ?

The general solution for 4sin(θ)+1=0 is θ=-0.25268…+2pin,θ=pi+0.25268…+2pin

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4sin(θ)+1=0

4 sin (θ) + 1 = 0

θ = - 0.25268 \dots + 2 πn, θ = π + 0.25268 \dots + 2 πn

Solution steps

4 sin (θ) + 1 = 0

Move

1

to the right side

4 sin (θ) = - 1

Divide both sides by

4

sin (θ) = - \frac{1}{4}

Apply trig inverse properties

θ = arcsin (- \frac{1}{4}) + 2 πn, θ = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

θ = - 0.25268 \dots + 2 πn, θ = π + 0.25268 \dots + 2 πn

sin^{2} (θ) (1 + csc^{2} (θ)) = k

- 3 cos (2 θ) + 9 cos (θ) - 7 = 4 cos (θ) - 3

sin (4 0^{\circ} - x) = cos (3 x)

y, e^{x} - sin (y) = x

cot (x) - tan (x) = 23

What is the general solution for 4sin(θ)+1=0 ?
The general solution for 4sin(θ)+1=0 is θ=-0.25268…+2pin,θ=pi+0.25268…+2pin