What is the general solution for 12cos^2(x)+11cos(x)-5=0 ?

The general solution for 12cos^2(x)+11cos(x)-5=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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12cos^2(x)+11cos(x)-5=0

12 cos^{2} (x) + 11 cos (x) - 5 = 0

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Solution steps

12 cos^{2} (x) + 11 cos (x) - 5 = 0

Solve by substitution

cos (x) = \frac{1}{3}, cos (x) = - \frac{5}{4}

cos (x) = \frac{1}{3} : x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

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

No Solution

Combine all the solutions

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

2 cos^{2} (x) + 3 cos (x) + 1 = 0, 0 \leq x \leq 2 π

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

21 + 18 cos (x) = 16 sin^{2} (x)

cot (θ - \frac{π}{2}) = 1.07, tan (θ)

sin (b) = 0.4848

What is the general solution for 12cos^2(x)+11cos(x)-5=0 ?
The general solution for 12cos^2(x)+11cos(x)-5=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin