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

The general solution for (cos(θ))/(sin(θ))=0 is θ= pi/2+pin

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(cos(θ))/(sin(θ))=0

\frac{cos ( θ )}{sin ( θ )} = 0

θ = \frac{π}{2} + πn

Degrees

θ = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

\frac{cos ( θ )}{sin ( θ )} = 0

Rewrite using trig identities

\frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

cot (θ) = 0

General solutions for

cot (θ) = 0

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

sin (2 x) = sin (x), 0 \leq x < 2 π

tan (θ) = \frac{5}{5 3}

7 cos (x) = 2 + 5 cos (x)

cos (x) = 7

5 sin (θ) cos (θ) + 4 cos (θ) = 0

What is the general solution for (cos(θ))/(sin(θ))=0 ?
The general solution for (cos(θ))/(sin(θ))=0 is θ= pi/2+pin