What is the general solution for cos(2x)=-0.32 ?

The general solution for cos(2x)=-0.32 is x=(1.89652…)/2+pin,x=-(1.89652…)/2+pin

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cos(2x)=-0.32

cos (2 x) = - 0.32

x = \frac{1.89652 \dots}{2} + πn, x = - \frac{1.89652 \dots}{2} + πn

Degrees

x = 54.33146 \dots^{\circ} + 18 0^{\circ} n, x = - 54.33146 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = - 0.32

Apply trig inverse properties

cos (2 x) = - 0.32

General solutions for

cos (2 x) = - 0.32

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

2 x = arccos (- 0.32) + 2 πn, 2 x = - arccos (- 0.32) + 2 πn

2 x = arccos (- 0.32) + 2 πn, 2 x = - arccos (- 0.32) + 2 πn

Solve

2 x = arccos (- 0.32) + 2 πn : x = \frac{arccos ( - 0.32 )}{2} + πn

2 x = arccos (- 0.32) + 2 πn

Divide both sides by

2

2 x = arccos (- 0.32) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( - 0.32 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( - 0.32 )}{2} + πn

x = \frac{arccos ( - 0.32 )}{2} + πn

Solve

2 x = - arccos (- 0.32) + 2 πn : x = - \frac{arccos ( - 0.32 )}{2} + πn

2 x = - arccos (- 0.32) + 2 πn

Divide both sides by

2

2 x = - arccos (- 0.32) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( - 0.32 )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arccos ( - 0.32 )}{2} + πn

x = - \frac{arccos ( - 0.32 )}{2} + πn

x = \frac{arccos ( - 0.32 )}{2} + πn, x = - \frac{arccos ( - 0.32 )}{2} + πn

Show solutions in decimal form

x = \frac{1.89652 \dots}{2} + πn, x = - \frac{1.89652 \dots}{2} + πn

sin (\frac{3 π}{2} - 0) = - cos (x)

sec (x) = - \frac{7}{4}

28 cos^{2} (θ) = 7

3 - cos (6 x) \cdot 6 = 0

sin (x) - cos (x) = 1, 0 \leq x \leq 36 0^{\circ}

What is the general solution for cos(2x)=-0.32 ?
The general solution for cos(2x)=-0.32 is x=(1.89652…)/2+pin,x=-(1.89652…)/2+pin