What is the general solution for sin(θ)-4=-5 ?

The general solution for sin(θ)-4=-5 is θ=(3pi)/2+2pin

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sin(θ)-4=-5

sin (θ) - 4 = - 5

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) - 4 = - 5

Move

4

to the right side

sin (θ) - 4 = - 5

Add

4

to both sides

sin (θ) - 4 + 4 = - 5 + 4

Simplify

sin (θ) = - 1

sin (θ) = - 1

General solutions for

sin (θ) = - 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

sin (θ) - 4 = - 3

csc^{2} (x) = 4 cot^{2} (x)

cot^{2} (3 x) - tan^{2} (3 x) = 0

x, cos (x) = 10

3 cos (θ) = 2, 1

What is the general solution for sin(θ)-4=-5 ?
The general solution for sin(θ)-4=-5 is θ=(3pi)/2+2pin