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

The general solution for 4cos^2(x)+7cos(x)=2 is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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4cos^2(x)+7cos(x)=2

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

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

Solution steps

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

Solve by substitution

cos (x) = \frac{1}{4}, cos (x) = - 2

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

cos (x) = - 2 :

No Solution

Combine all the solutions

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

Show solutions in decimal form

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

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

\frac{3}{5} = cos (x)

tan (θ) = \frac{36}{20 + 16}

tan (h) = \frac{9}{9 3}

arcsin (x) + arcsin (3 x) = \frac{π}{2}

What is the general solution for 4cos^2(x)+7cos(x)=2 ?
The general solution for 4cos^2(x)+7cos(x)=2 is x=1.31811…+2pin,x=2pi-1.31811…+2pin