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

The general solution for 5cos^2(x)+3cos(x)-2=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin,x=pi+2pin

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

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

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = \frac{2}{5} : x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn, x = π + 2 πn

sin (3 x) = sin (6 x)

tan^{3} (x) = 0

2 cos^{2} (x) = 11 cos (x) + 1

sin (x) sec (x) = 2 tan (x) - 1

sin (x) = sin (x + 3 0^{\circ})

What is the general solution for 5cos^2(x)+3cos(x)-2=0 ?
The general solution for 5cos^2(x)+3cos(x)-2=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin,x=pi+2pin