What is the general solution for cos(x)=(-3)/(sqrt(10)) ?

The general solution for cos(x)=(-3)/(sqrt(10)) is x=2.81984…+2pin,x=-2.81984…+2pin

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cos(x)=(-3)/(sqrt(10))

cos (x) = \frac{- 3}{10}

x = 2.81984 \dots + 2 πn, x = - 2.81984 \dots + 2 πn

Radians

x = 2.81984 \dots + 6.28318 \dots n, x = - 2.81984 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{- 3}{10}

Simplify

\frac{- 3}{10} : - \frac{3 10}{10}

\frac{- 3}{10}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{10}

Rationalize

- \frac{3}{10} : - \frac{3 10}{10}

- \frac{3}{10}

Multiply by the conjugate

\frac{10}{10}

= - \frac{3 10}{10 10}

1010 = 10

1010

Apply radical rule:

a a = a

1010 = 10

= 10

= - \frac{3 10}{10}

= - \frac{3 10}{10}

cos (x) = - \frac{3 10}{10}

Apply trig inverse properties

cos (x) = - \frac{3 10}{10}

General solutions for

cos (x) = - \frac{3 10}{10}

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

x = arccos (- \frac{3 10}{10}) + 2 πn, x = - arccos (- \frac{3 10}{10}) + 2 πn

x = arccos (- \frac{3 10}{10}) + 2 πn, x = - arccos (- \frac{3 10}{10}) + 2 πn

Show solutions in decimal form

x = 2.81984 \dots + 2 πn, x = - 2.81984 \dots + 2 πn

sin (θ) = \frac{21}{5}

sin (α) = \frac{3}{5}

x, tan^{2} (x) = 1

x, tan^{2} (x) = 2

x, \frac{p}{q} = sin^{2} (x)

What is the general solution for cos(x)=(-3)/(sqrt(10)) ?
The general solution for cos(x)=(-3)/(sqrt(10)) is x=2.81984…+2pin,x=-2.81984…+2pin