What is the general solution for 3+4sin(θ)=0 ?

The general solution for 3+4sin(θ)=0 is θ=-0.84806…+2pin,θ=pi+0.84806…+2pin

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3+4sin(θ)=0

3 + 4 sin (θ) = 0

θ = - 0.84806 \dots + 2 πn, θ = π + 0.84806 \dots + 2 πn

Degrees

θ = - 48.59037 \dots^{\circ} + 36 0^{\circ} n, θ = 228.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 + 4 sin (θ) = 0

Move

3

to the right side

3 + 4 sin (θ) = 0

Subtract

3

from both sides

3 + 4 sin (θ) - 3 = 0 - 3

Simplify

4 sin (θ) = - 3

4 sin (θ) = - 3

Divide both sides by

4

4 sin (θ) = - 3

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 3}{4}

Simplify

sin (θ) = - \frac{3}{4}

sin (θ) = - \frac{3}{4}

Apply trig inverse properties

sin (θ) = - \frac{3}{4}

General solutions for

sin (θ) = - \frac{3}{4}

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

θ = arcsin (- \frac{3}{4}) + 2 πn, θ = π + arcsin (\frac{3}{4}) + 2 πn

θ = arcsin (- \frac{3}{4}) + 2 πn, θ = π + arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = - 0.84806 \dots + 2 πn, θ = π + 0.84806 \dots + 2 πn

tan (2 A) = \frac{( 2 tan ( A ) )}{[ 1 + ( tan ( A ) ) ^{2} ]}

cos (4 x) + 1 = 3 sin (2 x)

tan (2 t + 15) = cot (6 t - 5)

3 sin (θ) = 0

2 cos^{3} (x) - cos^{2} (x) + 2 cos (x) - 1 = 0

What is the general solution for 3+4sin(θ)=0 ?
The general solution for 3+4sin(θ)=0 is θ=-0.84806…+2pin,θ=pi+0.84806…+2pin