What is the general solution for 9sin(θ)-7=0 ?

The general solution for 9sin(θ)-7=0 is θ=0.89112…+2pin,θ=pi-0.89112…+2pin

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9sin(θ)-7=0

9 sin (θ) - 7 = 0

θ = 0.89112 \dots + 2 πn, θ = π - 0.89112 \dots + 2 πn

Degrees

θ = 51.05755 \dots^{\circ} + 36 0^{\circ} n, θ = 128.94244 \dots^{\circ} + 36 0^{\circ} n

Solution steps

9 sin (θ) - 7 = 0

Move

7

to the right side

9 sin (θ) - 7 = 0

Add

7

to both sides

9 sin (θ) - 7 + 7 = 0 + 7

Simplify

9 sin (θ) = 7

9 sin (θ) = 7

Divide both sides by

9

9 sin (θ) = 7

Divide both sides by

9

\frac{9 sin ( θ )}{9} = \frac{7}{9}

Simplify

sin (θ) = \frac{7}{9}

sin (θ) = \frac{7}{9}

Apply trig inverse properties

sin (θ) = \frac{7}{9}

General solutions for

sin (θ) = \frac{7}{9}

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

θ = arcsin (\frac{7}{9}) + 2 πn, θ = π - arcsin (\frac{7}{9}) + 2 πn

θ = arcsin (\frac{7}{9}) + 2 πn, θ = π - arcsin (\frac{7}{9}) + 2 πn

Show solutions in decimal form

θ = 0.89112 \dots + 2 πn, θ = π - 0.89112 \dots + 2 πn

csc (2 x) = 2

sin (4 x) cos (x) - sin (x) cos (4 x) = \frac{3}{2}

7 sin (θ) + 1 = 5 sin (θ)

- 5 cos^{2} (θ) - 4 cos (θ) + 4 = 0

cos (x) = 0.159

What is the general solution for 9sin(θ)-7=0 ?
The general solution for 9sin(θ)-7=0 is θ=0.89112…+2pin,θ=pi-0.89112…+2pin