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

The general solution for cos(θ)-1=-1 is θ= pi/2+2pin,θ=(3pi)/2+2pin

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cos(θ)-1=-1

cos (θ) - 1 = - 1

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n, θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) - 1 = - 1

Add

1

to both sides

cos (θ) - 1 + 1 = - 1 + 1

Simplify

cos (θ) = 0

General solutions for

cos (θ) = 0

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 = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

2 = sec (θ)

csc^{2} (x) - 2 csc (x) = 0

sin^{2} (x) = - 1

25 tan^{2} (θ) - 4 = 0

tan (x) = \frac{8}{15}

What is the general solution for cos(θ)-1=-1 ?
The general solution for cos(θ)-1=-1 is θ= pi/2+2pin,θ=(3pi)/2+2pin