What is the general solution for -5sin^2(θ)+17cos(θ)+9=4cos(θ)-2 ?

The general solution for -5sin^2(θ)+17cos(θ)+9=4cos(θ)-2 is θ=2.21429…+2pin,θ=-2.21429…+2pin

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-5sin^2(θ)+17cos(θ)+9=4cos(θ)-2

- 5 sin^{2} (θ) + 17 cos (θ) + 9 = 4 cos (θ) - 2

θ = 2.21429 \dots + 2 πn, θ = - 2.21429 \dots + 2 πn

Solution steps

- 5 sin^{2} (θ) + 17 cos (θ) + 9 = 4 cos (θ) - 2

Subtract

4 cos (θ) - 2

from both sides

13 cos (θ) - 5 sin^{2} (θ) + 11 = 0

Rewrite using trig identities

6 + 13 cos (θ) + 5 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = - \frac{3}{5}, cos (θ) = - 2

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

cos (θ) = - 2 :

No Solution

Combine all the solutions

θ = arccos (- \frac{3}{5}) + 2 πn, θ = - arccos (- \frac{3}{5}) + 2 πn

Show solutions in decimal form

θ = 2.21429 \dots + 2 πn, θ = - 2.21429 \dots + 2 πn

(cos (3 θ)) (cos (θ)) + 1 = (sin (3 θ)) (sin (θ))

4 sin (x) - 3 = 0

9 sin (x) tan (x) = 2 tan (x)

- 5 sin (2 x) = 0

- 2 sin^{2} (x) = - sin (x) - 1

What is the general solution for -5sin^2(θ)+17cos(θ)+9=4cos(θ)-2 ?
The general solution for -5sin^2(θ)+17cos(θ)+9=4cos(θ)-2 is θ=2.21429…+2pin,θ=-2.21429…+2pin