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

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

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(sin(θ))/(cos(θ))=0

\frac{sin ( θ )}{cos ( θ )} = 0

θ = πn

Degrees

θ = 0^{\circ} + 18 0^{\circ} n

Solution steps

\frac{sin ( θ )}{cos ( θ )} = 0

Rewrite using trig identities

\frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

tan (θ) = 0

General solutions for

tan (θ) = 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}

θ = 0 + πn

θ = 0 + πn

Solve

θ = 0 + πn : θ = πn

θ = 0 + πn

0 + πn = πn

θ = πn

θ = πn

0 = sin (y)

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

tan^{2} (x) - sec^{2} (x) = cos (- x)

sec^{2} (θ) tan (θ) = 2 tan (θ), 0 \leq θ \leq 2 π

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

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