What is the general solution for sin(2x)-sqrt(3)cos(2x)=0 ?

The general solution for sin(2x)-sqrt(3)cos(2x)=0 is x= pi/6+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)-sqrt(3)cos(2x)=0

Solution

sin (2 x) - 3 cos (2 x) = 0

Solution

x = \frac{π}{6} + \frac{πn}{2}

Degrees

x = 3 0^{\circ} + 9 0^{\circ} n

Solution steps

sin (2 x) - 3 cos (2 x) = 0

Rewrite using trig identities

sin (2 x) - 3 cos (2 x) = 0

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

\frac{sin ( 2 x ) - 3 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

\frac{sin ( 2 x )}{cos ( 2 x )} - 3 = 0

Use the basic trigonometric identity:

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

tan (2 x) - 3 = 0

tan (2 x) - 3 = 0

Move

3

to the right side

tan (2 x) - 3 = 0

Add

3

to both sides

tan (2 x) - 3 + 3 = 0 + 3

Simplify

tan (2 x) = 3

tan (2 x) = 3

General solutions for

tan (2 x) = 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}

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

Solve

2 x = \frac{π}{3} + πn : x = \frac{π}{6} + \frac{πn}{2}

2 x = \frac{π}{3} + πn

Divide both sides by

2

2 x = \frac{π}{3} + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{3}}{2} + \frac{πn}{2} : \frac{π}{6} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

Popular Examples

3sin(2x)=3cos(x)

3 sin (2 x) = 3 cos (x)

4sec(x)+8=0

4 sec (x) + 8 = 0

solvefor x,ln(y)=e^ysin(x)solve for

x, ln (y) = e^{y} sin (x)

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

2 sin^{2} (x) = 1 - sin (x)

tan(x)sin(2x)=0

tan (x) sin (2 x) = 0

Frequently Asked Questions (FAQ)

What is the general solution for sin(2x)-sqrt(3)cos(2x)=0 ?
The general solution for sin(2x)-sqrt(3)cos(2x)=0 is x= pi/6+(pin)/2