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

The general solution for sin(θ)=2cos(θ) is θ=1.10714…+pin

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sin(θ)=2cos(θ)

sin (θ) = 2 cos (θ)

θ = 1.10714 \dots + πn

Degrees

θ = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (θ) = 2 cos (θ)

Rewrite using trig identities

sin (θ) = 2 cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{sin ( θ )}{cos ( θ )} = \frac{2 cos ( θ )}{cos ( θ )}

Simplify

\frac{sin ( θ )}{cos ( θ )} = 2

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (θ) = 2

tan (θ) = 2

Apply trig inverse properties

tan (θ) = 2

General solutions for

tan (θ) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (2) + πn

θ = arctan (2) + πn

Show solutions in decimal form

θ = 1.10714 \dots + πn

2 cos^{2} (w) + 5 cos (w) + 3 = 0

tan (x) = - 135

3 cos (x) - 4 sin (x) = - 3

6 = 50 sin (x) - 15 cos (x), 0 < x < \frac{π}{2}

y, x = 3 sin (y)

What is the general solution for sin(θ)=2cos(θ) ?
The general solution for sin(θ)=2cos(θ) is θ=1.10714…+pin