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

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

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

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

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

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

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

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

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