What is the general solution for (sin(θ))/(cos(θ))=1 ?

The general solution for (sin(θ))/(cos(θ))=1 is θ= pi/4+pin

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(sin(θ))/(cos(θ))=1

\frac{sin ( θ )}{cos ( θ )} = 1

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

\frac{sin ( θ )}{cos ( θ )} = 1

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) = 1

General solutions for

tan (θ) = 1

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 = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

What is the general solution for (sin(θ))/(cos(θ))=1 ?
The general solution for (sin(θ))/(cos(θ))=1 is θ= pi/4+pin