What is the general solution for 4cos^2(x)-11cos(x)+6=0 ?

The general solution for 4cos^2(x)-11cos(x)+6=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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4cos^2(x)-11cos(x)+6=0

4 cos^{2} (x) - 11 cos (x) + 6 = 0

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Solution steps

4 cos^{2} (x) - 11 cos (x) + 6 = 0

Solve by substitution

cos (x) = 2, cos (x) = \frac{3}{4}

cos (x) = 2 :

No Solution

cos (x) = \frac{3}{4} : x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Combine all the solutions

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

tanh (x) = 0.99

3 cos (3 0^{\circ}) + 4 cos (y) = 3

tan (y) = \frac{6}{4}

cos (x) = \frac{- 1 + 5}{4}

t, a = 5 \cdot sin (t)

What is the general solution for 4cos^2(x)-11cos(x)+6=0 ?
The general solution for 4cos^2(x)-11cos(x)+6=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin