What is the general solution for -4=(sin(θ))/(cos(θ)) ?

The general solution for -4=(sin(θ))/(cos(θ)) is θ=-1.32581…+pin

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-4=(sin(θ))/(cos(θ))

- 4 = \frac{sin ( θ )}{cos ( θ )}

θ = - 1.32581 \dots + πn

Degrees

θ = - 75.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 4 = \frac{sin ( θ )}{cos ( θ )}

Switch sides

\frac{sin ( θ )}{cos ( θ )} = - 4

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) = - 4

Apply trig inverse properties

tan (θ) = - 4

General solutions for

tan (θ) = - 4

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- 4) + πn

θ = arctan (- 4) + πn

Show solutions in decimal form

θ = - 1.32581 \dots + πn

What is the general solution for -4=(sin(θ))/(cos(θ)) ?
The general solution for -4=(sin(θ))/(cos(θ)) is θ=-1.32581…+pin