What is the general solution for 4cos(2x)-3=0 ?

The general solution for 4cos(2x)-3=0 is x=(0.72273…)/2+pin,x=pi-(0.72273…)/2+pin

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4cos(2x)-3=0

4 cos (2 x) - 3 = 0

x = \frac{0.72273 \dots}{2} + πn, x = π - \frac{0.72273 \dots}{2} + πn

Degrees

x = 20.70481 \dots^{\circ} + 18 0^{\circ} n, x = 159.29518 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 cos (2 x) - 3 = 0

Move

3

to the right side

4 cos (2 x) - 3 = 0

Add

3

to both sides

4 cos (2 x) - 3 + 3 = 0 + 3

Simplify

4 cos (2 x) = 3

4 cos (2 x) = 3

Divide both sides by

4

4 cos (2 x) = 3

Divide both sides by

4

\frac{4 cos ( 2 x )}{4} = \frac{3}{4}

Simplify

cos (2 x) = \frac{3}{4}

cos (2 x) = \frac{3}{4}

Apply trig inverse properties

cos (2 x) = \frac{3}{4}

General solutions for

cos (2 x) = \frac{3}{4}

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

2 x = arccos (\frac{3}{4}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{4}) + 2 πn

2 x = arccos (\frac{3}{4}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{4}) + 2 πn

Solve

2 x = arccos (\frac{3}{4}) + 2 πn : x = \frac{arccos ( \frac{3}{4} )}{2} + πn

2 x = arccos (\frac{3}{4}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{3}{4}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{3}{4} )}{2} + πn

x = \frac{arccos ( \frac{3}{4} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{3}{4}) + 2 πn : x = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

2 x = 2 π - arccos (\frac{3}{4}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{3}{4}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

x = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

x = \frac{arccos ( \frac{3}{4} )}{2} + πn, x = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

Show solutions in decimal form

x = \frac{0.72273 \dots}{2} + πn, x = π - \frac{0.72273 \dots}{2} + πn

sin^{2} (x) + 1 = 0

cos (t) - sin (2 t) = 0

sin (2 x - \frac{π}{2}) = - 1

3 tan^{2} (2 x) = 1

tan (x) + cot (x) = 3

What is the general solution for 4cos(2x)-3=0 ?
The general solution for 4cos(2x)-3=0 is x=(0.72273…)/2+pin,x=pi-(0.72273…)/2+pin