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

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

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Popular >

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

Solution

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

Solution

x = \frac{π}{3} + \frac{πn}{2}

Degrees

x = 6 0^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 + tan (2 x) = 0

3 + tan (2 x) = 0

Move

3

to the right side

3 + tan (2 x) = 0

Subtract

3

from both sides

3 + tan (2 x) - 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{2 π}{3} + πn

2 x = \frac{2 π}{3} + πn

Solve

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

2 x = \frac{2 π}{3} + πn

Divide both sides by

2

2 x = \frac{2 π}{3} + πn

Divide both sides by

2

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

Simplify

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

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

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

Apply the fraction rule:

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

= \frac{2 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

Popular Examples

cos((-pi)/2+x/2)=0

cos (\frac{- π}{2} + \frac{x}{2}) = 0

cos(x)=-0.175

cos (x) = - 0.175

sec^2(x)=2tan^2(x)

sec^{2} (x) = 2 tan^{2} (x)

(sin(x))/(cos(x))-5+(4cos(x))/(sin(x))=0

\frac{sin ( x )}{cos ( x )} - 5 + \frac{4 cos ( x )}{sin ( x )} = 0

solvefor x,y=sin(3.2x)solve for

x, y = sin (3.2 x)

Frequently Asked Questions (FAQ)

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