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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(θ))/(cos(θ))=sqrt(3)

\frac{sin ( θ )}{cos ( θ )} = 3

θ = \frac{π}{3} + πn

Degrees

θ = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

\frac{sin ( θ )}{cos ( θ )} = 3

Rewrite using trig identities

\frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

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

48 sin^{2} (x) = 48 - 24 cos (x)

1 - 4 cos (2 x) = 0

\frac{1}{2} = cos (θ)

tan^{2} (x) + 5 tan (x) = 0

1 - sinh^{2} (x) = 0

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