What is the general solution for cos(2x)=-17/81 ?

The general solution for cos(2x)=-17/81 is x=(1.78224…)/2+pin,x=-(1.78224…)/2+pin

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cos(2x)=-17/81

cos (2 x) = - \frac{17}{81}

x = \frac{1.78224 \dots}{2} + πn, x = - \frac{1.78224 \dots}{2} + πn

Degrees

x = 51.05755 \dots^{\circ} + 18 0^{\circ} n, x = - 51.05755 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = - \frac{17}{81}

Apply trig inverse properties

cos (2 x) = - \frac{17}{81}

General solutions for

cos (2 x) = - \frac{17}{81}

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

2 x = arccos (- \frac{17}{81}) + 2 πn, 2 x = - arccos (- \frac{17}{81}) + 2 πn

2 x = arccos (- \frac{17}{81}) + 2 πn, 2 x = - arccos (- \frac{17}{81}) + 2 πn

Solve

2 x = arccos (- \frac{17}{81}) + 2 πn : x = \frac{arccos ( - \frac{17}{81} )}{2} + πn

2 x = arccos (- \frac{17}{81}) + 2 πn

Divide both sides by

2

2 x = arccos (- \frac{17}{81}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( - \frac{17}{81} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( - \frac{17}{81} )}{2} + πn

x = \frac{arccos ( - \frac{17}{81} )}{2} + πn

Solve

2 x = - arccos (- \frac{17}{81}) + 2 πn : x = - \frac{arccos ( - \frac{17}{81} )}{2} + πn

2 x = - arccos (- \frac{17}{81}) + 2 πn

Divide both sides by

2

2 x = - arccos (- \frac{17}{81}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( - \frac{17}{81} )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arccos ( - \frac{17}{81} )}{2} + πn

x = - \frac{arccos ( - \frac{17}{81} )}{2} + πn

x = \frac{arccos ( - \frac{17}{81} )}{2} + πn, x = - \frac{arccos ( - \frac{17}{81} )}{2} + πn

Show solutions in decimal form

x = \frac{1.78224 \dots}{2} + πn, x = - \frac{1.78224 \dots}{2} + πn

sin^{2} (θ) + cos (2 θ) = 0

csc (θ) = \frac{28}{2}, sin (θ)

\frac{1 + csc ( γ )}{cot ( γ ) + cos ( γ )} = csc (γ)

sin (θ) = \frac{2}{6}

3 sin (2 x) = - 2

What is the general solution for cos(2x)=-17/81 ?
The general solution for cos(2x)=-17/81 is x=(1.78224…)/2+pin,x=-(1.78224…)/2+pin