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

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

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cos(2x)= 3/4

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

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

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 (x) = 0.7, 0^{\circ} \leq x \leq 36 0^{\circ}

- 2 + cot (θ) = - 3, 0 \leq θ < 2 π

sec (θ) csc (θ) = 2 csc (θ)

sin (A) = \frac{( 60 ) sin ( 15 5 ^{\circ} )}{97.73}

cos (θ) = 1 - cos (θ)

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