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

The general solution for cos^2(x)-5cos(x)+2=0 is x=1.11692…+2pin,x=2pi-1.11692…+2pin

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

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

x = 1.11692 \dots + 2 πn, x = 2 π - 1.11692 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{5 + 17}{2}, cos (x) = \frac{5 - 17}{2}

cos (x) = \frac{5 + 17}{2} :

No Solution

cos (x) = \frac{5 - 17}{2} : x = arccos (\frac{5 - 17}{2}) + 2 πn, x = 2 π - arccos (\frac{5 - 17}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{5 - 17}{2}) + 2 πn, x = 2 π - arccos (\frac{5 - 17}{2}) + 2 πn

Show solutions in decimal form

x = 1.11692 \dots + 2 πn, x = 2 π - 1.11692 \dots + 2 πn

2 sin^{2} (θ) + 3 sin (θ) = 4 sin (θ) + 1

cos (θ - \frac{π}{6}) = \frac{3}{2}

csc (θ) = - \frac{5}{3}

2 sin^{2} (t) cos (t) = 0

2 cos (θ) + sin (θ) = 0

What is the general solution for cos^2(x)-5cos(x)+2=0 ?
The general solution for cos^2(x)-5cos(x)+2=0 is x=1.11692…+2pin,x=2pi-1.11692…+2pin