What is the general solution for -6=-5+cos(θ) ?

The general solution for -6=-5+cos(θ) is θ=pi+2pin

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-6=-5+cos(θ)

- 6 = - 5 + cos (θ)

θ = π + 2 πn

Degrees

θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

- 6 = - 5 + cos (θ)

Switch sides

- 5 + cos (θ) = - 6

Move

5

to the right side

- 5 + cos (θ) = - 6

Add

5

to both sides

- 5 + cos (θ) + 5 = - 6 + 5

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

tan (x) = - 26, \frac{3 π}{2} < x < 2 π

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

tan^{2} (x) - 4 sec (x) = 4

sin (x + 1 0^{\circ}) = - tan (1 5^{\circ})

tan (2 θ) = \frac{73 - 8}{- 10}

What is the general solution for -6=-5+cos(θ) ?
The general solution for -6=-5+cos(θ) is θ=pi+2pin