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

The general solution for cos(x)=sqrt(2/2) is x=2pin

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cos(x)=sqrt(2/2)

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

x = 2 πn

Radians

x = 0 + 2 πn

Solution steps

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

Simplify

\frac{2}{2} : 1

\frac{2}{2}

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

= 1

Apply rule

1 = 1

= 1

General solutions for

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

21.16 = 19.6 sin (x) - 29.4 cos (x)

10 sin (x) cos^{2} (x) + 3 cos (x) = 0

(2 cos (x)) - 1 = 0

3 cos (x) = sin^{2} (x)

sin (θ) = \frac{5 π}{3}

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