What is the general solution for solvefor θ,2cos^2(θ)+9cos(θ)-5=0 ?

The general solution for solvefor θ,2cos^2(θ)+9cos(θ)-5=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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solvefor θ,2cos^2(θ)+9cos(θ)-5=0

solve for

θ, 2 cos^{2} (θ) + 9 cos (θ) - 5 = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

2 cos^{2} (θ) + 9 cos (θ) - 5 = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 5

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

cos (θ) = - 5 :

No Solution

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

tan (3 x) = - 3, 0 \leq x \leq 2 π

5 cos (θ) = - 3

sec^{2} (x) - sec (x) = 0

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

3 cos (x) = \frac{6}{π}

What is the general solution for solvefor θ,2cos^2(θ)+9cos(θ)-5=0 ?
The general solution for solvefor θ,2cos^2(θ)+9cos(θ)-5=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin