What is the general solution for 3cos^2(x)-4cos(x)+1=0 ?

The general solution for 3cos^2(x)-4cos(x)+1=0 is x=2pin,x=1.23095…+2pin,x=2pi-1.23095…+2pin

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3cos^2(x)-4cos(x)+1=0

3 cos^{2} (x) - 4 cos (x) + 1 = 0

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

Solution steps

3 cos^{2} (x) - 4 cos (x) + 1 = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

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

cos (x) = 0.1

3 tan (x) = 2.4568

cos (x) = 1.5

\frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

8 cos (B) + 52 = 0

What is the general solution for 3cos^2(x)-4cos(x)+1=0 ?
The general solution for 3cos^2(x)-4cos(x)+1=0 is x=2pin,x=1.23095…+2pin,x=2pi-1.23095…+2pin