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

The general solution for sin(2θ)=3cos(2θ) is θ=(1.24904…)/2+(pin)/2

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sin(2θ)=3cos(2θ)

sin (2 θ) = 3 cos (2 θ)

θ = \frac{1.24904 \dots}{2} + \frac{πn}{2}

Solution steps

sin (2 θ) = 3 cos (2 θ)

Rewrite using trig identities

tan (2 θ) = 3

Apply trig inverse properties

2 θ = arctan (3) + πn

Solve

2 θ = arctan (3) + πn : θ = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.24904 \dots}{2} + \frac{πn}{2}

1 - cos (2 x) = sin (2 x)

cos (θ) = 5

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

x, tan (3 x) = 5 tan (x)

3 sin (2 t) = 0

What is the general solution for sin(2θ)=3cos(2θ) ?
The general solution for sin(2θ)=3cos(2θ) is θ=(1.24904…)/2+(pin)/2