What is the general solution for 8cos(2x)=1 ?

The general solution for 8cos(2x)=1 is x=(1.44546…)/2+pin,x=pi-(1.44546…)/2+pin

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8cos(2x)=1

8 cos (2 x) = 1

x = \frac{1.44546 \dots}{2} + πn, x = π - \frac{1.44546 \dots}{2} + πn

Degrees

x = 41.40962 \dots^{\circ} + 18 0^{\circ} n, x = 138.59037 \dots^{\circ} + 18 0^{\circ} n

Solution steps

8 cos (2 x) = 1

Divide both sides by

8

8 cos (2 x) = 1

Divide both sides by

8

\frac{8 cos ( 2 x )}{8} = \frac{1}{8}

Simplify

cos (2 x) = \frac{1}{8}

cos (2 x) = \frac{1}{8}

Apply trig inverse properties

cos (2 x) = \frac{1}{8}

General solutions for

cos (2 x) = \frac{1}{8}

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

2 x = arccos (\frac{1}{8}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{8}) + 2 πn

2 x = arccos (\frac{1}{8}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{8}) + 2 πn

Solve

2 x = arccos (\frac{1}{8}) + 2 πn : x = \frac{arccos ( \frac{1}{8} )}{2} + πn

2 x = arccos (\frac{1}{8}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{1}{8}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{1}{8} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{1}{8} )}{2} + πn

x = \frac{arccos ( \frac{1}{8} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{1}{8}) + 2 πn : x = π - \frac{arccos ( \frac{1}{8} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{8}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{1}{8}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{8} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{1}{8} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{8} )}{2} + πn

x = \frac{arccos ( \frac{1}{8} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{8} )}{2} + πn

Show solutions in decimal form

x = \frac{1.44546 \dots}{2} + πn, x = π - \frac{1.44546 \dots}{2} + πn

cos (- (\frac{π}{6}) - 2 x) = 1

csc (x) = 6

(sin (x))^{s i n (x)} = 2

cos^{2} (x) + \frac{1}{2} + sin^{2} (x) + \frac{1}{2} = 2

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

What is the general solution for 8cos(2x)=1 ?
The general solution for 8cos(2x)=1 is x=(1.44546…)/2+pin,x=pi-(1.44546…)/2+pin