What is the general solution for cos(2θ)+3sin(θ)=2 ?

The general solution for cos(2θ)+3sin(θ)=2 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin

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cos(2θ)+3sin(θ)=2

cos (2 θ) + 3 sin (θ) = 2

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

Solution steps

cos (2 θ) + 3 sin (θ) = 2

Subtract

2

from both sides

cos (2 θ) + 3 sin (θ) - 2 = 0

Rewrite using trig identities

- 1 - 2 sin^{2} (θ) + 3 sin (θ) = 0

Solve by substitution

sin (θ) = \frac{1}{2}, sin (θ) = 1

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

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

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

sec^{2} (\frac{x}{3}) = 2

sin (w) = 0.79

tan^{2} (x) - tan (x) = 0, [0 \leq x < 2 π]

arcsin (x) = 0.5

What is the general solution for cos(2θ)+3sin(θ)=2 ?
The general solution for cos(2θ)+3sin(θ)=2 is θ= pi/6+2pin,θ=(5pi)/6+2pin,θ= pi/2+2pin