What is the general solution for 3cos^2(x)-8cos(x)+4=0 ?

The general solution for 3cos^2(x)-8cos(x)+4=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin

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3cos^2(x)-8cos(x)+4=0

3 cos^{2} (x) - 8 cos (x) + 4 = 0

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Solution steps

3 cos^{2} (x) - 8 cos (x) + 4 = 0

Solve by substitution

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

cos (x) = 2 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

sin^{(2)} (x) - sin (x) = 1 - sin^{(2)} (x)

49.55 \cdot 1 - sin^{2} (θ) - 30 sin (θ) = 1.225

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

x, e^{c o s (y)} - e^{s i n (x)} = sin (y)

5 + tan (θ) = 4

What is the general solution for 3cos^2(x)-8cos(x)+4=0 ?
The general solution for 3cos^2(x)-8cos(x)+4=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin