What is the general solution for 4cos^2(x)-7cos(x)+3=0 ?

The general solution for 4cos^2(x)-7cos(x)+3=0 is x=2pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin

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4cos^2(x)-7cos(x)+3=0

4 cos^{2} (x) - 7 cos (x) + 3 = 0

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

Solution steps

4 cos^{2} (x) - 7 cos (x) + 3 = 0

Solve by substitution

cos (x) = 1, cos (x) = \frac{3}{4}

cos (x) = 1 : x = 2 πn

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

Show solutions in decimal form

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

tan (θ) = \frac{- \frac{4}{3} - ( - \frac{11}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

8 + 2 cot (x) = 12

(1 + cot (p)) tan (p) = 3

csc (θ + π) = - \frac{2 3}{3}

sin (x) = \frac{33}{105}

What is the general solution for 4cos^2(x)-7cos(x)+3=0 ?
The general solution for 4cos^2(x)-7cos(x)+3=0 is x=2pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin