What is the general solution for cos(x)=-1/(5sqrt(2)) ?

The general solution for cos(x)=-1/(5sqrt(2)) is x=1.71269…+2pin,x=-1.71269…+2pin

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cos(x)=-1/(5sqrt(2))

cos (x) = - \frac{1}{5 2}

x = 1.71269 \dots + 2 πn, x = - 1.71269 \dots + 2 πn

Radians

x = 1.71269 \dots + 6.28318 \dots n, x = - 1.71269 \dots + 6.28318 \dots n

Solution steps

cos (x) = - \frac{1}{5 2}

Simplify

- \frac{1}{5 2} : - \frac{2}{10}

- \frac{1}{5 2}

Multiply by the conjugate

\frac{2}{2}

= - \frac{1 \cdot 2}{5 2 2}

1 \cdot 2 = 2

522 = 10

522

Apply radical rule:

a a = a

22 = 2

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

= - \frac{2}{10}

cos (x) = - \frac{2}{10}

Apply trig inverse properties

cos (x) = - \frac{2}{10}

General solutions for

cos (x) = - \frac{2}{10}

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

x = arccos (- \frac{2}{10}) + 2 πn, x = - arccos (- \frac{2}{10}) + 2 πn

x = arccos (- \frac{2}{10}) + 2 πn, x = - arccos (- \frac{2}{10}) + 2 πn

Show solutions in decimal form

x = 1.71269 \dots + 2 πn, x = - 1.71269 \dots + 2 πn

What is the general solution for cos(x)=-1/(5sqrt(2)) ?
The general solution for cos(x)=-1/(5sqrt(2)) is x=1.71269…+2pin,x=-1.71269…+2pin