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

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

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sqrt(3)cos(θ)=sin(θ)

3 cos (θ) = sin (θ)

θ = \frac{π}{3} + πn

Degrees

θ = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (θ) = sin (θ)

Rewrite using trig identities

3 cos (θ) = sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{3 cos ( θ )}{cos ( θ )} = \frac{sin ( θ )}{cos ( θ )}

Simplify

3 = \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

3 = tan (θ)

Switch sides

tan (θ) = 3

tan (θ) = 3

General solutions for

tan (θ) = 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

csc (θ) = \frac{4}{3}

9^{s i n (x) - 1} + 3 = 3^{s i n (x)} + 3^{s i n (x) - 1}

3 + 3 sin (θ) = 9 sin (θ)

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

5 sin (3 x) = - 2

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