What is the general solution for cos(x)= 1/(sqrt(5)) ?

The general solution for cos(x)= 1/(sqrt(5)) is x=1.10714…+2pin,x=2pi-1.10714…+2pin

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cos(x)= 1/(sqrt(5))

cos (x) = \frac{1}{5}

x = 1.10714 \dots + 2 πn, x = 2 π - 1.10714 \dots + 2 πn

Radians

x = 1.10714 \dots + 6.28318 \dots n, x = 5.17603 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{1}{5}

Simplify

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

Multiply by the conjugate

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= \frac{5}{5}

cos (x) = \frac{5}{5}

Apply trig inverse properties

cos (x) = \frac{5}{5}

General solutions for

cos (x) = \frac{5}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{5}{5}) + 2 πn, x = 2 π - arccos (\frac{5}{5}) + 2 πn

x = arccos (\frac{5}{5}) + 2 πn, x = 2 π - arccos (\frac{5}{5}) + 2 πn

Show solutions in decimal form

x = 1.10714 \dots + 2 πn, x = 2 π - 1.10714 \dots + 2 πn

3 tan (3 x) + 1 = 0

2 tan (θ) - 3 = 0

csc^{2} (x) - cot (x) = 1

cos (2 x) - 3 sin (x) = 2

tan (θ) = 9

What is the general solution for cos(x)= 1/(sqrt(5)) ?
The general solution for cos(x)= 1/(sqrt(5)) is x=1.10714…+2pin,x=2pi-1.10714…+2pin