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

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

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

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

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

Solution steps

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

Show solutions in decimal form

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

arctan (θ) = - 2

sin (3 x) - sin (x) = sin (3 x - x)

sin (a) = - \frac{3}{2}

t, v = 311 cos (30 t + 3 0^{\circ}) v

cos^{2} (x) = 2 sin (x)

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