What is the general solution for 5cos^2(x)+6cos(x)=8 ?

The general solution for 5cos^2(x)+6cos(x)=8 is x=0.64350…+2pin,x=2pi-0.64350…+2pin

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5cos^2(x)+6cos(x)=8

5 cos^{2} (x) + 6 cos (x) = 8

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn

Solution steps

5 cos^{2} (x) + 6 cos (x) = 8

Solve by substitution

cos (x) = \frac{4}{5}, cos (x) = - 2

cos (x) = \frac{4}{5} : x = arccos (\frac{4}{5}) + 2 πn, x = 2 π - arccos (\frac{4}{5}) + 2 πn

cos (x) = - 2 :

No Solution

Combine all the solutions

x = arccos (\frac{4}{5}) + 2 πn, x = 2 π - arccos (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn

tan (x) = \frac{- 4}{3}

sin (x) = \frac{2.5}{5}

3 cos^{2} (x) = 0

tan (4 x) = 2 tan (2 x)

sec (x) - 4 = - sec (x)

What is the general solution for 5cos^2(x)+6cos(x)=8 ?
The general solution for 5cos^2(x)+6cos(x)=8 is x=0.64350…+2pin,x=2pi-0.64350…+2pin