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

The general solution for cos(4x)= 2/3 is x=(0.84106…)/4+(pin)/2 ,x= pi/2-(0.84106…)/4+(pin)/2

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cos(4x)= 2/3

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

x = \frac{0.84106 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.84106 \dots}{4} + \frac{πn}{2}

Solution steps

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{0.84106 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.84106 \dots}{4} + \frac{πn}{2}

- 1 + cos (θ) = cos (2 θ)

3 cos (θ) = 3 sin (- θ)

3 tan (\frac{2 x}{3}) + 1 = 0

sin (x) = \frac{11}{61}

sin^{3} (x) = - sin^{2} (x)

What is the general solution for cos(4x)= 2/3 ?
The general solution for cos(4x)= 2/3 is x=(0.84106…)/4+(pin)/2 ,x= pi/2-(0.84106…)/4+(pin)/2