What is the general solution for 3cos^2(x)-8cos(x)-3=0 ?

The general solution for 3cos^2(x)-8cos(x)-3=0 is x=1.91063…+2pin,x=-1.91063…+2pin

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3cos^2(x)-8cos(x)-3=0

3 cos^{2} (x) - 8 cos (x) - 3 = 0

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

Solution steps

3 cos^{2} (x) - 8 cos (x) - 3 = 0

Solve by substitution

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

cos (x) = 3 :

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 (x) + sin (x) = 2

12 sin (c) + 6 = 5 sin (c) + 6

2 cos^{2} (t) - cos (t) - 1 = 0

sin (x) = - \frac{8}{17}

1 - 2 cos (θ) = 0

What is the general solution for 3cos^2(x)-8cos(x)-3=0 ?
The general solution for 3cos^2(x)-8cos(x)-3=0 is x=1.91063…+2pin,x=-1.91063…+2pin