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

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

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-cos(x)=cos(-x)

- cos (x) = cos (- x)

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

Degrees

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

Solution steps

- cos (x) = cos (- x)

Rewrite using trig identities

- cos (x) = cos (- x)

- cos (x) = cos (x)

- cos (x) = cos (x)

Subtract

cos (x)

from both sides

- 2 cos (x) = 0

Divide both sides by

- 2

- 2 cos (x) = 0

Divide both sides by

- 2

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

Simplify

cos (x) = 0

cos (x) = 0

General solutions for

cos (x) = 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}

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

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

5 sin (θ) + 1 = 3 sin (θ)

sin (x) = 1 + cos (x)

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

sin (2 x) = 0.8

cot (x) = tan (x)

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