What is the general solution for cos(θ)=(-1)/2 ?

The general solution for cos(θ)=(-1)/2 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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cos(θ)=(-1)/2

cos (θ) = \frac{- 1}{2}

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Degrees

θ = 12 0^{\circ} + 36 0^{\circ} n, θ = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{- 1}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

cos (θ) = - \frac{1}{2}

General solutions for

cos (θ) = - \frac{1}{2}

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{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

2 sin (x) sec (x) = 2 sin (x)

tan^{3} (x) = tan (x)

3 - 2 sin (x) = 0

- 9 cos^{2} (θ) + 14 sin (θ) + 14 = 0

cos (x) tan (x) = - 7 tan (x)

What is the general solution for cos(θ)=(-1)/2 ?
The general solution for cos(θ)=(-1)/2 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin