What is the general solution for pi/6 =cos(2x) ?

The general solution for pi/6 =cos(2x) is x=(1.01972…)/2+pin,x=pi-(1.01972…)/2+pin

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pi/6 =cos(2x)

\frac{π}{6} = cos (2 x)

x = \frac{1.01972 \dots}{2} + πn, x = π - \frac{1.01972 \dots}{2} + πn

Degrees

x = 29.21301 \dots^{\circ} + 18 0^{\circ} n, x = 150.78698 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{π}{6} = cos (2 x)

Switch sides

cos (2 x) = \frac{π}{6}

Apply trig inverse properties

cos (2 x) = \frac{π}{6}

General solutions for

cos (2 x) = \frac{π}{6}

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

2 x = arccos (\frac{π}{6}) + 2 πn, 2 x = 2 π - arccos (\frac{π}{6}) + 2 πn

2 x = arccos (\frac{π}{6}) + 2 πn, 2 x = 2 π - arccos (\frac{π}{6}) + 2 πn

Solve

2 x = arccos (\frac{π}{6}) + 2 πn : x = \frac{arccos ( \frac{π}{6} )}{2} + πn

2 x = arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{π}{6} )}{2} + πn

x = \frac{arccos ( \frac{π}{6} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{π}{6}) + 2 πn : x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

2 x = 2 π - arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{π}{6}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

x = \frac{arccos ( \frac{π}{6} )}{2} + πn, x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

Show solutions in decimal form

x = \frac{1.01972 \dots}{2} + πn, x = π - \frac{1.01972 \dots}{2} + πn

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tan (2 y) = 1

(- 6 cos (x) + 2 sin (x))^{2} + 32 sin^{2} (x) = 48

tan (x) + 5 = \frac{15 - 3}{3}

5 cos^{2} (x) - cos (x) - sin^{2} (x) = 0

What is the general solution for pi/6 =cos(2x) ?
The general solution for pi/6 =cos(2x) is x=(1.01972…)/2+pin,x=pi-(1.01972…)/2+pin