What is the general solution for 6cos(2x)=5 ?

The general solution for 6cos(2x)=5 is x=(0.58568…)/2+pin,x=pi-(0.58568…)/2+pin

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6cos(2x)=5

6 cos (2 x) = 5

x = \frac{0.58568 \dots}{2} + πn, x = π - \frac{0.58568 \dots}{2} + πn

Degrees

x = 16.77865 \dots^{\circ} + 18 0^{\circ} n, x = 163.22134 \dots^{\circ} + 18 0^{\circ} n

Solution steps

6 cos (2 x) = 5

Divide both sides by

6

6 cos (2 x) = 5

Divide both sides by

6

\frac{6 cos ( 2 x )}{6} = \frac{5}{6}

Simplify

cos (2 x) = \frac{5}{6}

cos (2 x) = \frac{5}{6}

Apply trig inverse properties

cos (2 x) = \frac{5}{6}

General solutions for

cos (2 x) = \frac{5}{6}

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

2 x = arccos (\frac{5}{6}) + 2 πn, 2 x = 2 π - arccos (\frac{5}{6}) + 2 πn

2 x = arccos (\frac{5}{6}) + 2 πn, 2 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

2 x = arccos (\frac{5}{6}) + 2 πn : x = \frac{arccos ( \frac{5}{6} )}{2} + πn

2 x = arccos (\frac{5}{6}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{5}{6}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{5}{6} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{5}{6} )}{2} + πn

x = \frac{arccos ( \frac{5}{6} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{5}{6}) + 2 πn : x = π - \frac{arccos ( \frac{5}{6} )}{2} + πn

2 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{5}{6} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{5}{6} )}{2} + πn

x = π - \frac{arccos ( \frac{5}{6} )}{2} + πn

x = \frac{arccos ( \frac{5}{6} )}{2} + πn, x = π - \frac{arccos ( \frac{5}{6} )}{2} + πn

Show solutions in decimal form

x = \frac{0.58568 \dots}{2} + πn, x = π - \frac{0.58568 \dots}{2} + πn

2 cos^{2} (2 x) = 1

sin (z) = \frac{1}{2}

sin (3 x) = \frac{- 1}{2}

4 cos^{2} (x) + 7 sin (x) - 2 = 0

sin (3 x) = - \frac{2}{2}

What is the general solution for 6cos(2x)=5 ?
The general solution for 6cos(2x)=5 is x=(0.58568…)/2+pin,x=pi-(0.58568…)/2+pin