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

The general solution for cos(x)=-1/(sqrt(5)) is x=2.03444…+2pin,x=-2.03444…+2pin

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

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

x = 2.03444 \dots + 2 πn, x = - 2.03444 \dots + 2 πn

Radians

x = 2.03444 \dots + 6.28318 \dots n, x = - 2.03444 \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 = - arccos (- a) + 2 πn

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

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

Show solutions in decimal form

x = 2.03444 \dots + 2 πn, x = - 2.03444 \dots + 2 πn

What is the general solution for cos(x)=-1/(sqrt(5)) ?
The general solution for cos(x)=-1/(sqrt(5)) is x=2.03444…+2pin,x=-2.03444…+2pin