What is the general solution for cos(2x)=-0.6 ?

The general solution for cos(2x)=-0.6 is x=(2.21429…)/2+pin,x=-(2.21429…)/2+pin

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cos(2x)=-0.6

cos (2 x) = - 0.6

x = \frac{2.21429 \dots}{2} + πn, x = - \frac{2.21429 \dots}{2} + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n, x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = - 0.6

Apply trig inverse properties

cos (2 x) = - 0.6

General solutions for

cos (2 x) = - 0.6

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

2 x = arccos (- 0.6) + 2 πn, 2 x = - arccos (- 0.6) + 2 πn

2 x = arccos (- 0.6) + 2 πn, 2 x = - arccos (- 0.6) + 2 πn

Solve

2 x = arccos (- 0.6) + 2 πn : x = \frac{arccos ( - 0.6 )}{2} + πn

2 x = arccos (- 0.6) + 2 πn

Divide both sides by

2

2 x = arccos (- 0.6) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( - 0.6 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( - 0.6 )}{2} + πn

x = \frac{arccos ( - 0.6 )}{2} + πn

Solve

2 x = - arccos (- 0.6) + 2 πn : x = - \frac{arccos ( - 0.6 )}{2} + πn

2 x = - arccos (- 0.6) + 2 πn

Divide both sides by

2

2 x = - arccos (- 0.6) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( - 0.6 )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arccos ( - 0.6 )}{2} + πn

x = - \frac{arccos ( - 0.6 )}{2} + πn

x = \frac{arccos ( - 0.6 )}{2} + πn, x = - \frac{arccos ( - 0.6 )}{2} + πn

Show solutions in decimal form

x = \frac{2.21429 \dots}{2} + πn, x = - \frac{2.21429 \dots}{2} + πn

2 sin (x) - cos (x) = 0

2 cos (x) = sin (2 x)

sec (θ) + 1 = 0

tan (x) = \frac{5}{4}

sin (x) tan (x) = - 10 tan (x)

What is the general solution for cos(2x)=-0.6 ?
The general solution for cos(2x)=-0.6 is x=(2.21429…)/2+pin,x=-(2.21429…)/2+pin