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

The general solution for cos(2x)= 2/3 is x=(0.84106…)/2+pin,x=pi-(0.84106…)/2+pin

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cos(2x)= 2/3

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

x = \frac{0.84106 \dots}{2} + πn, x = π - \frac{0.84106 \dots}{2} + πn

Solution steps

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{0.84106 \dots}{2} + πn, x = π - \frac{0.84106 \dots}{2} + πn

- cos (7 x) + cos (3 x) = sin (5 x)

2 sin (θ) - 3 csc (θ) + 5 = 0

csc^{4} (2 x) - 4 = 0

sin (θ) = \frac{4}{13}

sin (3 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

What is the general solution for cos(2x)= 2/3 ?
The general solution for cos(2x)= 2/3 is x=(0.84106…)/2+pin,x=pi-(0.84106…)/2+pin