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

The general solution for cos(x)=((sqrt(2)))/2 is x= pi/4+2pin,x=(7pi)/4+2pin

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

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

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

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{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

\frac{sin ( x )}{cos ( x )} + \frac{cos ( x )}{sec ( x )} = 1

csc^{2} (x) = 5 csc (x) + 6

tan (θ) = 1770

2 sin^{2} (x) - \frac{5}{4} = - cos^{2} (x)

23 sin (2 x) = 3

What is the general solution for cos(x)=((sqrt(2)))/2 ?
The general solution for cos(x)=((sqrt(2)))/2 is x= pi/4+2pin,x=(7pi)/4+2pin