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

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

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3cos(x)=2

3 cos (x) = 2

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

Degrees

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) = 2

Divide both sides by

3

3 cos (x) = 2

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

4 tan (θ) + 1 = 0

0 = - 3 sin (x)

5 sin (x) - 1 = 0

sec^{2} (x) = 4 tan (x) - 2

sin (x) = 2 sin (x) cos (x)

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