How to find the inverse tangent since the calculator is limited

This is probably a basic concept that I just never really grasped...now I'm in Calc III and it's biting me in the butt.

I need to find theta = arctan(-1/2)

I typed it into my calculator to receive the answer **-.464 radians**

But calculators are limited when it comes to solving trig, and as I understand there are other answers other than what I received. How do I go about finding the other answer(s)?

Re: How to find the inverse tangent since the calculator is limited

Quote:

Originally Posted by

**TWN** This is probably a basic concept that I just never really grasped...now I'm in Calc III and it's biting me in the butt.

I need to find theta = arctan(-1/2)

I typed it into my calculator to receive the answer **-.464 radians**

But calculators are limited when it comes to solving trig, and as I understand there are other answers other than what I received. How do I go about finding the other answer(s)?

This is equivalent to $\displaystyle \displaystyle \begin{align*} \tan{\theta} = -\frac{1}{2} \end{align*}$. The tangent function has a period of $\displaystyle \displaystyle \begin{align*} \pi \end{align*}$, so to get the general solution, you need to write $\displaystyle \displaystyle \begin{align*} + \pi n \end{align*}$ where $\displaystyle \displaystyle \begin{align*} n \in \mathbf{Z} \end{align*}$ after $\displaystyle \displaystyle \begin{align*} -0.464 \end{align*}$.

Re: How to find the inverse tangent since the calculator is limited

Quote:

Originally Posted by

**Prove It** This is equivalent to $\displaystyle \displaystyle \begin{align*} \tan{\theta} = -\frac{1}{2} \end{align*}$. The tangent function has a period of $\displaystyle \displaystyle \begin{align*} \pi \end{align*}$, so to get the general solution, you need to write $\displaystyle \displaystyle \begin{align*} + \pi n \end{align*}$ where $\displaystyle \displaystyle \begin{align*} n \in \mathbf{Z} \end{align*}$ after $\displaystyle \displaystyle \begin{align*} -0.464 \end{align*}$.

You started speaking a language I don't understand in the end there.

Re: How to find the inverse tangent since the calculator is limited

You can look up some math proof-symbols to find some of the common ones. What Prove It said there is: -0.464 + pi*n where n is an element of the real numbers.