Question

Find all solutions to the equation

tan(theta)+sqrt3=0

Write your answer in terms of pi and use the or button as necessary.

Answer 1

\[example \theta=\frac{ 2\pi }{ 5 }k \pi, k \epsilon \]

Answer 2

Rewrite the given equation by subtracting Sqrt(3) from both sides.

Answer 3

\[\theta=\frac{ 5\pi }{ 3 }\pm \pi n, or \frac{ 2\pi }{ 3 }\pm \pi n?\]

Answer 4

I was hoping you'd rewrite the given equation by subtracting Sqrt (3) from both sides:
\[\tan(\theta)+\sqrt3=0\rightarrow \tan \theta=\frac{ -\sqrt{3} }{ 1 }\]

If you do this, then the problem boils down to determining which angles have the tangent equal to \[\frac{ -\sqrt{3} }{ 1 }\] Please explain how you got from that to your possible answers.

Answer 5

Hint: because the tangent is negative, the angles in question MUST be in Q2 and Q4. Does this make sense to you?

Answer 6

Note that 2Pi/3 and 5Pi/3 are in Q2 and Q4 respectively. But how did you obtain these angles?