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=1.91063…+2pin,x=-1.91063…+2pin,x=pi+2pin

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

Show solutions in decimal form

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

cos^{5} (x) = \frac{1}{2}

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

5 sec (x) - 4 cos (x) = 8

sin^{3} (x) = - 1

x, sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

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=1.91063…+2pin,x=-1.91063…+2pin,x=pi+2pin