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

The general solution for 2sin(θ)=cos(θ) is θ=0.46364…+pin

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2sin(θ)=cos(θ)

2 sin (θ) = cos (θ)

θ = 0.46364 \dots + πn

Degrees

θ = 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (θ) = cos (θ)

Rewrite using trig identities

2 sin (θ) = cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

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

Simplify

\frac{2 sin ( θ )}{cos ( θ )} = 1

Use the basic trigonometric identity:

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

2 tan (θ) = 1

2 tan (θ) = 1

Divide both sides by

2

2 tan (θ) = 1

Divide both sides by

2

\frac{2 tan ( θ )}{2} = \frac{1}{2}

Simplify

tan (θ) = \frac{1}{2}

tan (θ) = \frac{1}{2}

Apply trig inverse properties

tan (θ) = \frac{1}{2}

General solutions for

tan (θ) = \frac{1}{2}

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

θ = arctan (\frac{1}{2}) + πn

θ = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

θ = 0.46364 \dots + πn

2 cos (x) = - 1

2 sec (u) sin (u) + 2 = 4 sin (u) + sec (u)

4 cos^{2} (x) - 1 = 0, 0 \leq x < 2 π

y, e^{2 x} = sin (x + 3 y)

7 sin (2 x) = 7 cos (x)

What is the general solution for 2sin(θ)=cos(θ) ?
The general solution for 2sin(θ)=cos(θ) is θ=0.46364…+pin