What is the general solution for 5cos(3x)=-4 ?

The general solution for 5cos(3x)=-4 is x=(2.49809…)/3+(2pin)/3 ,x=-(2.49809…)/3+(2pin)/3

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5cos(3x)=-4

5 cos (3 x) = - 4

x = \frac{2.49809 \dots}{3} + \frac{2 πn}{3}, x = - \frac{2.49809 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 47.71003 \dots^{\circ} + 12 0^{\circ} n, x = - 47.71003 \dots^{\circ} + 12 0^{\circ} n

Solution steps

5 cos (3 x) = - 4

Divide both sides by

5

5 cos (3 x) = - 4

Divide both sides by

5

\frac{5 cos ( 3 x )}{5} = \frac{- 4}{5}

Simplify

cos (3 x) = - \frac{4}{5}

cos (3 x) = - \frac{4}{5}

Apply trig inverse properties

cos (3 x) = - \frac{4}{5}

General solutions for

cos (3 x) = - \frac{4}{5}

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

3 x = arccos (- \frac{4}{5}) + 2 πn, 3 x = - arccos (- \frac{4}{5}) + 2 πn

3 x = arccos (- \frac{4}{5}) + 2 πn, 3 x = - arccos (- \frac{4}{5}) + 2 πn

Solve

3 x = arccos (- \frac{4}{5}) + 2 πn : x = \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = arccos (- \frac{4}{5}) + 2 πn

Divide both sides by

3

3 x = arccos (- \frac{4}{5}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

Solve

3 x = - arccos (- \frac{4}{5}) + 2 πn : x = - \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = - arccos (- \frac{4}{5}) + 2 πn

Divide both sides by

3

3 x = - arccos (- \frac{4}{5}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = - \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

Simplify

x = - \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = - \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}, x = - \frac{arccos ( - \frac{4}{5} )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{2.49809 \dots}{3} + \frac{2 πn}{3}, x = - \frac{2.49809 \dots}{3} + \frac{2 πn}{3}

What is the general solution for 5cos(3x)=-4 ?
The general solution for 5cos(3x)=-4 is x=(2.49809…)/3+(2pin)/3 ,x=-(2.49809…)/3+(2pin)/3