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

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

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2/3 =cos(x)

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

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Solution steps

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

Switch sides

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

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

2 cos (\frac{x}{2}) - 3 = 0

cos (2 x) + 3 cos (x) = 1

cos (2 θ) - cos (θ) = 2

sin (θ) - cos^{2} (θ) sin (θ) = - 1

5 sin (2 θ) - 2 sin (θ) = 0

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