What is the general solution for ((sin(5x)))/((-1cos(5x)))=0 ?

The general solution for ((sin(5x)))/((-1cos(5x)))=0 is x=(pin)/5

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((sin(5x)))/((-1cos(5x)))=0

\frac{( sin ( 5 x ) )}{( - 1 cos ( 5 x ) )} = 0

x = \frac{πn}{5}

Degrees

x = 0^{\circ} + 3 6^{\circ} n

Solution steps

\frac{( sin ( 5 x ) )}{( - 1 \cdot cos ( 5 x ) )} = 0

Rewrite using trig identities

\frac{sin ( 5 x )}{- 1 \cdot cos ( 5 x )}

Use the basic trigonometric identity:

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

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

\frac{tan ( 5 x )}{- 1} = 0

Multiply both sides by

- 1

\frac{tan ( 5 x )}{- 1} = 0

Multiply both sides by

- 1

\frac{tan ( 5 x ) ( - 1 )}{- 1} = 0 \cdot (- 1)

Simplify

tan (5 x) = 0

tan (5 x) = 0

General solutions for

tan (5 x) = 0

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}

5 x = 0 + πn

5 x = 0 + πn

Solve

5 x = 0 + πn : x = \frac{πn}{5}

5 x = 0 + πn

0 + πn = πn

5 x = πn

Divide both sides by

5

5 x = πn

Divide both sides by

5

\frac{5 x}{5} = \frac{πn}{5}

Simplify

x = \frac{πn}{5}

x = \frac{πn}{5}

x = \frac{πn}{5}

sin (x) = cos (4 0^{\circ})

tan (x) = \frac{2.5}{2}

sin (2 x) cos (x) + sin (x) cos (2 x) = - \frac{1}{2}

5 cos (x) + 2 = 3 cos (x), 0 \leq x \leq 2 π

2 tan (2 x + 10) = - 5.5

What is the general solution for ((sin(5x)))/((-1cos(5x)))=0 ?
The general solution for ((sin(5x)))/((-1cos(5x)))=0 is x=(pin)/5