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

The general solution for cos(3x)-sin(3x)=0 is x= pi/(12)+(pin)/3

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Popular Trigonometry >

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

Solution

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

Solution

x = \frac{π}{12} + \frac{πn}{3}

Degrees

x = 1 5^{\circ} + 6 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (3 x), cos (3 x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

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

1 - tan (3 x) = 0

1 - tan (3 x) = 0

Move

1

to the right side

1 - tan (3 x) = 0

Subtract

1

from both sides

1 - tan (3 x) - 1 = 0 - 1

Simplify

- tan (3 x) = - 1

- tan (3 x) = - 1

Divide both sides by

- 1

- tan (3 x) = - 1

Divide both sides by

- 1

\frac{- tan ( 3 x )}{- 1} = \frac{- 1}{- 1}

Simplify

tan (3 x) = 1

tan (3 x) = 1

General solutions for

tan (3 x) = 1

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}

3 x = \frac{π}{4} + πn

3 x = \frac{π}{4} + πn

Solve

3 x = \frac{π}{4} + πn : x = \frac{π}{12} + \frac{πn}{3}

3 x = \frac{π}{4} + πn

Divide both sides by

3

3 x = \frac{π}{4} + πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{3} + \frac{πn}{3} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for cos(3x)-sin(3x)=0 ?
The general solution for cos(3x)-sin(3x)=0 is x= pi/(12)+(pin)/3