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

The general solution for (cos(θ))/(sin(θ))=-1 is θ=(3pi)/4+pin

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(cos(θ))/(sin(θ))=-1

\frac{cos ( θ )}{sin ( θ )} = - 1

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

\frac{cos ( θ )}{sin ( θ )} = - 1

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) = - 1

General solutions for

cot (θ) = - 1

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{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

cos (B) = \frac{12}{13}

sin (θ) = \frac{2}{9}, θ, 3 r (θ, d) d, tan (2 θ)

sin (\frac{x}{2}) = 0, 0 \leq x \leq 2 π

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

(2 sin (x) - 1) (sin (x) + 0.5) = 0

What is the general solution for (cos(θ))/(sin(θ))=-1 ?
The general solution for (cos(θ))/(sin(θ))=-1 is θ=(3pi)/4+pin