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

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

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sin(2θ)=3cos(θ)

sin (2 θ) = 3 cos (θ)

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

Solution steps

sin (2 θ) = 3 cos (θ)

Subtract

3 cos (θ)

from both sides

sin (2 θ) - 3 cos (θ) = 0

Rewrite using trig identities

- 3 cos (θ) + 2 cos (θ) sin (θ) = 0

Factor

- 3 cos (θ) + 2 cos (θ) sin (θ) : cos (θ) (2 sin (θ) - 3)

cos (θ) (2 sin (θ) - 3) = 0

Solving each part separately

cos (θ) = 0 or 2 sin (θ) - 3 = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

2 sin (θ) - 3 = 0 :

No Solution

Combine all the solutions

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

x, tan (x) + ∣ tan (x) ∣ = 1

0 = 2 sin^{2} (θ) + 3 sin (θ)

y, x = arctan (x + y)

2 sin (2 x) = 3 tan (x)

tan (φ) = \frac{1}{3}

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