-9cos^2(θ)+sin(θ)+11=-sin(θ)+2

Solution

- 9 cos^{2} (θ) + sin (θ) + 11 = - sin (θ) + 2

θ = 2 πn, θ = π + 2 πn, θ = - 0.22409 \dots + 2 πn, θ = π + 0.22409 \dots + 2 πn

Solution steps

- 9 cos^{2} (θ) + sin (θ) + 11 = - sin (θ) + 2

Subtract

- sin (θ) + 2

from both sides

2 sin (θ) - 9 cos^{2} (θ) + 9 = 0

Rewrite using trig identities

2 sin (θ) + 9 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = 0, sin (θ) = - \frac{2}{9}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = - \frac{2}{9} : θ = arcsin (- \frac{2}{9}) + 2 πn, θ = π + arcsin (\frac{2}{9}) + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = arcsin (- \frac{2}{9}) + 2 πn, θ = π + arcsin (\frac{2}{9}) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = π + 2 πn, θ = - 0.22409 \dots + 2 πn, θ = π + 0.22409 \dots + 2 πn

sin (θ) = 1 - 2 cos (θ)

6 sec^{2} (x) - 6 sec (x) = 12

sin (a) = \frac{2}{2}

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

cos^{2} (x) + 2 sin (x) + 2 = 0