What is the general solution for 3cos^2(x)-5cos(x)-2=0 ?

The general solution for 3cos^2(x)-5cos(x)-2=0 is x=1.91063…+2pin,x=-1.91063…+2pin

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3cos^2(x)-5cos(x)-2=0

3 cos^{2} (x) - 5 cos (x) - 2 = 0

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Solution steps

3 cos^{2} (x) - 5 cos (x) - 2 = 0

Solve by substitution

cos (x) = 2, cos (x) = - \frac{1}{3}

cos (x) = 2 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

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

sin (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

4 cos^{2} (x) + 2 cos (x) = 2, 0 \leq x \leq 2 π

arctan (x) + arctan (2 x) = \frac{π}{4}

1 + cos (θ) = \frac{2 + 3}{2}

What is the general solution for 3cos^2(x)-5cos(x)-2=0 ?
The general solution for 3cos^2(x)-5cos(x)-2=0 is x=1.91063…+2pin,x=-1.91063…+2pin