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Popular >

-3cos(2θ)-sin(θ)-6=-8

Solution

- 3 cos (2 θ) - sin (θ) - 6 = - 8

Solution

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

+1

Solution steps

- 3 cos (2 θ) - sin (θ) - 6 = - 8

Subtract

- 8

from both sides

- 3 cos (2 θ) - sin (θ) + 2 = 0

Rewrite using trig identities

- 1 - sin (θ) + 6 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = \frac{1}{2}, sin (θ) = - \frac{1}{3}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = - \frac{1}{3} : θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

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