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

The general solution for 3cos^2(x)+4cos(x)-4=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin

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

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

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Solution steps

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

Solve by substitution

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

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

cos (x) = - 2 :

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

sin (θ) = - \frac{27}{190}

4 sin (θ) = 1 + sin (θ)

tan (θ) - 3 = 0, 0 \leq θ \leq 2 π

\frac{1}{32} \cdot 120 0^{2} \cdot sin (2 θ) = 3000

1 - cos^{2} (a) = sin^{2} (2 a)

What is the general solution for 3cos^2(x)+4cos(x)-4=0 ?
The general solution for 3cos^2(x)+4cos(x)-4=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin