What is the general solution for -4cos^2(x)+3cos(x)+1=0 ?

The general solution for -4cos^2(x)+3cos(x)+1=0 is x=1.82347…+2pin,x=-1.82347…+2pin,x=2pin

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-4cos^2(x)+3cos(x)+1=0

- 4 cos^{2} (x) + 3 cos (x) + 1 = 0

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn, x = 2 πn

Solution steps

- 4 cos^{2} (x) + 3 cos (x) + 1 = 0

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn, x = 2 πn

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

105 = 100 + 30 sin (\frac{12 π}{5} t)

\frac{3}{sin ( x )} = \frac{1}{cos ( x )}

2 cos (t) - 2 sin (2 t) = 0

4 sin (x) = - 2 cos (x)

What is the general solution for -4cos^2(x)+3cos(x)+1=0 ?
The general solution for -4cos^2(x)+3cos(x)+1=0 is x=1.82347…+2pin,x=-1.82347…+2pin,x=2pin