What is the general solution for 4cos^2(x)+3cos(x)=1 ?

The general solution for 4cos^2(x)+3cos(x)=1 is x=1.31811…+2pin,x=2pi-1.31811…+2pin,x=pi+2pin

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4cos^2(x)+3cos(x)=1

4 cos^{2} (x) + 3 cos (x) = 1

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn, x = π + 2 πn

Solution steps

4 cos^{2} (x) + 3 cos (x) = 1

Solve by substitution

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

cos (x) = \frac{1}{4} : x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn, x = π + 2 πn

sin (x) = 4 cos (x)

7 cos (x) = 0

sin (θ) = \frac{3 13}{13}, sec (θ)

sin (y) = \frac{1}{2}

3 sin^{2} (x) = 5 sin (x) + 2

What is the general solution for 4cos^2(x)+3cos(x)=1 ?
The general solution for 4cos^2(x)+3cos(x)=1 is x=1.31811…+2pin,x=2pi-1.31811…+2pin,x=pi+2pin