What is the general solution for 3cos^2(x)-5cos(x)-2=0,(0,360) ?

The general solution for 3cos^2(x)-5cos(x)-2=0,(0,360) is x=1.91063…,x=-1.91063…+360

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3cos^2(x)-5cos(x)-2=0,(0,360)

3 cos^{2} (x) - 5 cos (x) - 2 = 0, (0^{\circ}, 36 0^{\circ})

x = 1.91063 \dots, x = - 1.91063 \dots + 36 0^{\circ}

Solution steps

3 cos^{2} (x) - 5 cos (x) - 2 = 0, (0^{\circ}, 36 0^{\circ})

Solve by substitution

cos (x) = 2, cos (x) = - \frac{1}{3}

cos (x) = 2, (0, 36 0^{\circ}) :

No Solution

cos (x) = - \frac{1}{3}, (0, 36 0^{\circ}) : x = arccos (- \frac{1}{3}), x = - arccos (- \frac{1}{3}) + 36 0^{\circ}

Combine all the solutions

x = arccos (- \frac{1}{3}), x = - arccos (- \frac{1}{3}) + 36 0^{\circ}

Show solutions in decimal form

x = 1.91063 \dots, x = - 1.91063 \dots + 36 0^{\circ}

3 - 5 cos (x) = 0

9 cos (2 θ) = 0

cos (A) = \frac{2}{3}

2 sin (θ) = 3 (1 - cos (θ))

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

What is the general solution for 3cos^2(x)-5cos(x)-2=0,(0,360) ?
The general solution for 3cos^2(x)-5cos(x)-2=0,(0,360) is x=1.91063…,x=-1.91063…+360