What is the general solution for cos(θ)= 5/(5sqrt(2)) ?

The general solution for cos(θ)= 5/(5sqrt(2)) is θ= pi/4+2pin,θ=(7pi)/4+2pin

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cos(θ)= 5/(5sqrt(2))

cos (θ) = \frac{5}{5 2}

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

Solution steps

cos (θ) = \frac{5}{5 2}

Simplify

\frac{5}{5 2} : \frac{2}{2}

\frac{5}{5 2}

Divide the numbers:

\frac{5}{5} = 1

= \frac{1}{2}

Rationalize

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

= \frac{2}{2}

cos (θ) = \frac{2}{2}

General solutions for

cos (θ) = \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}

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

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

arccos (x) = arcsin (\frac{9}{41})

x, - y sin (x) = 0

2 sin (\frac{x}{2} + \frac{π}{3}) = 3

x, 4 sin^{4} (x) - 8 sin^{2} (x) + 3 = 0

3 + 3 sin (θ) = 3 - 3 sin (θ)

What is the general solution for cos(θ)= 5/(5sqrt(2)) ?
The general solution for cos(θ)= 5/(5sqrt(2)) is θ= pi/4+2pin,θ=(7pi)/4+2pin