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=1.18933…+2pin,x=2pi-1.18933…+2pin

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

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

x = 1.18933 \dots + 2 πn, x = 2 π - 1.18933 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 5 + 33}{2}, cos (x) = \frac{- 5 - 33}{2}

cos (x) = \frac{- 5 + 33}{2} : x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

cos (x) = \frac{- 5 - 33}{2} :

No Solution

Combine all the solutions

x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

Show solutions in decimal form

x = 1.18933 \dots + 2 πn, x = 2 π - 1.18933 \dots + 2 πn

cos (2 x) + cos (2 x) + 1 = 0

(cos^{2} (x) + cos (x)) \cdot (sin (x) + sin^{3} (x)) = 0

arccos (x) - arcsin (x) = arcsin (1 - x)

sin^{2} (x) = ∣ sin (x) ∣

1 - cos^{2} (x) - sin^{22} (x) = 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=1.18933…+2pin,x=2pi-1.18933…+2pin