What is the general solution for 3cos(3x)-15sin(3x)=0 ?

The general solution for 3cos(3x)-15sin(3x)=0 is x=(0.19739…)/3+(pin)/3

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Popular Trigonometry >

3cos(3x)-15sin(3x)=0

Solution

3 cos (3 x) - 15 sin (3 x) = 0

Solution

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

Degrees

x = 3.76997 \dots^{\circ} + 6 0^{\circ} n

Solution steps

3 cos (3 x) - 15 sin (3 x) = 0

Rewrite using trig identities

3 cos (3 x) - 15 sin (3 x) = 0

Divide both sides by

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

\frac{3 cos ( 3 x ) - 15 sin ( 3 x )}{cos ( 3 x )} = \frac{0}{cos ( 3 x )}

Simplify

3 - \frac{15 sin ( 3 x )}{cos ( 3 x )} = 0

Use the basic trigonometric identity:

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

3 - 15 tan (3 x) = 0

3 - 15 tan (3 x) = 0

Move

3

to the right side

3 - 15 tan (3 x) = 0

Subtract

3

from both sides

3 - 15 tan (3 x) - 3 = 0 - 3

Simplify

- 15 tan (3 x) = - 3

- 15 tan (3 x) = - 3

Divide both sides by

- 15

- 15 tan (3 x) = - 3

Divide both sides by

- 15

\frac{- 15 tan ( 3 x )}{- 15} = \frac{- 3}{- 15}

Simplify

\frac{- 15 tan ( 3 x )}{- 15} = \frac{- 3}{- 15}

Simplify

\frac{- 15 tan ( 3 x )}{- 15} : tan (3 x)

\frac{- 15 tan ( 3 x )}{- 15}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{15 tan ( 3 x )}{15}

Divide the numbers:

\frac{15}{15} = 1

= tan (3 x)

Simplify

\frac{- 3}{- 15} : \frac{1}{5}

\frac{- 3}{- 15}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3}{15}

Cancel the common factor:

3

= \frac{1}{5}

tan (3 x) = \frac{1}{5}

tan (3 x) = \frac{1}{5}

tan (3 x) = \frac{1}{5}

Apply trig inverse properties

tan (3 x) = \frac{1}{5}

General solutions for

tan (3 x) = \frac{1}{5}

tan (x) = a \Rightarrow x = arctan (a) + πn

3 x = arctan (\frac{1}{5}) + πn

3 x = arctan (\frac{1}{5}) + πn

Solve

3 x = arctan (\frac{1}{5}) + πn : x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

3 x = arctan (\frac{1}{5}) + πn

Divide both sides by

3

3 x = arctan (\frac{1}{5}) + πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

Simplify

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 3cos(3x)-15sin(3x)=0 ?
The general solution for 3cos(3x)-15sin(3x)=0 is x=(0.19739…)/3+(pin)/3