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

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

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7-7sin(θ)=7

7 - 7 sin (θ) = 7

θ = 2 πn, θ = π + 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

7 - 7 sin (θ) = 7

Subtract

7

from both sides

7 - 7 sin (θ) - 7 = 7 - 7

Simplify

- 7 sin (θ) = 0

Divide both sides by

- 7

- 7 sin (θ) = 0

Divide both sides by

- 7

\frac{- 7 sin ( θ )}{- 7} = \frac{0}{- 7}

Simplify

sin (θ) = 0

sin (θ) = 0

General solutions for

sin (θ) = 0

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 = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

- 12 cos^{2} (θ) - 8 = - 17

2 cos (\frac{1}{2} x) - 2 = 0

cos (\frac{π}{x}) = 0

tan^{2} (θ) - 4 sec (θ) = - 5

tan (θ) = \frac{5}{6}

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