What is the general solution for cos(x)+(sqrt(2))/2 =0 ?

The general solution for cos(x)+(sqrt(2))/2 =0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin

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cos(x)+(sqrt(2))/2 =0

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

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Degrees

x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n

Solution steps

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

Move

\frac{2}{2}

to the right side

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

Subtract

\frac{2}{2}

from both sides

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

Simplify

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

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

General solutions for

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

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

(6 cos (x) - 5 sin (x))^{2} + 11 sin^{2} (x) = 36

e^{s i n (x)} - 2 = 0

(3 cos (x) - 6 sin (x))^{2} - 27 sin^{2} (x) = - 9

cos (2 x) = \frac{( 3 k - 2 )}{3}

sin^{2} (x) - sin (x) = 0, ([0, 2 π])

What is the general solution for cos(x)+(sqrt(2))/2 =0 ?
The general solution for cos(x)+(sqrt(2))/2 =0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin