What is the general solution for 3cos(x)=1 ?

The general solution for 3cos(x)=1 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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3cos(x)=1

3 cos (x) = 1

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Degrees

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) = 1

Divide both sides by

3

3 cos (x) = 1

Divide both sides by

3

\frac{3 cos ( x )}{3} = \frac{1}{3}

Simplify

cos (x) = \frac{1}{3}

cos (x) = \frac{1}{3}

Apply trig inverse properties

cos (x) = \frac{1}{3}

General solutions for

cos (x) = \frac{1}{3}

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

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

cos (a) = \frac{4}{5}

5 - 10 sin^{2} (x) = 0

sec^{2} (θ) - 2 = 0

2 - sin^{2} (x) = 2 cos^{2} (\frac{x}{2})

sec (\frac{θ}{5}) = 10

What is the general solution for 3cos(x)=1 ?
The general solution for 3cos(x)=1 is x=1.23095…+2pin,x=2pi-1.23095…+2pin