What is the general solution for 1-7cos(θ)=8 ?

The general solution for 1-7cos(θ)=8 is θ=pi+2pin

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1-7cos(θ)=8

1 - 7 cos (θ) = 8

θ = π + 2 πn

Degrees

θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

1 - 7 cos (θ) = 8

Move

1

to the right side

1 - 7 cos (θ) = 8

Subtract

1

from both sides

1 - 7 cos (θ) - 1 = 8 - 1

Simplify

- 7 cos (θ) = 7

- 7 cos (θ) = 7

Divide both sides by

- 7

- 7 cos (θ) = 7

Divide both sides by

- 7

\frac{- 7 cos ( θ )}{- 7} = \frac{7}{- 7}

Simplify

cos (θ) = - 1

cos (θ) = - 1

General solutions for

cos (θ) = - 1

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = π + 2 πn

θ = π + 2 πn

tanh (x) = \frac{12}{13}

sin (θ) = \frac{5}{7}

8 sin^{2} (x) + 2 sin (x) - 1 = 0

2 sin^{2} (x) = 5 sin (x) - 3

cos (x) cos (3 x) = sin (x) sin (3 x)

What is the general solution for 1-7cos(θ)=8 ?
The general solution for 1-7cos(θ)=8 is θ=pi+2pin