What is the general solution for 2sin(θ)-cos(θ)=0 ?

The general solution for 2sin(θ)-cos(θ)=0 is θ=0.46364…+pin

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2sin(θ)-cos(θ)=0

2 sin (θ) - cos (θ) = 0

θ = 0.46364 \dots + πn

Degrees

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

Solution steps

2 sin (θ) - cos (θ) = 0

Rewrite using trig identities

2 sin (θ) - cos (θ) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{2 sin ( θ ) - cos ( θ )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

\frac{2 sin ( θ )}{cos ( θ )} - 1 = 0

Use the basic trigonometric identity:

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

2 tan (θ) - 1 = 0

2 tan (θ) - 1 = 0

Move

1

to the right side

2 tan (θ) - 1 = 0

Add

1

to both sides

2 tan (θ) - 1 + 1 = 0 + 1

Simplify

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

cot (\frac{x}{7}) = 12

sin (θ) = \frac{4}{9}

y, x = sec (y)

2 cos^{2} (θ) - cos (θ) - 4 = - 6 cos (θ) - 6

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

What is the general solution for 2sin(θ)-cos(θ)=0 ?
The general solution for 2sin(θ)-cos(θ)=0 is θ=0.46364…+pin