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

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

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(sin(x))/(cos(x))=0

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

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

tan (x) = 0

General solutions for

tan (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}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

sin^{2} (x) - cos^{2} (x) + cos (x) = 0

8 cos (x) - 42 = 0

3 csc (x) - 23 = 0

x, arccos (x) = \frac{1}{2}

cos (2 x) = \frac{1}{5}

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