# How to find the inverse tangent since the calculator is limited

• October 3rd 2012, 12:51 AM
TWN
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)

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)?
• October 3rd 2012, 01:17 AM
Prove It
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)

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 \begin{align*} \tan{\theta} = -\frac{1}{2} \end{align*}. The tangent function has a period of \displaystyle \begin{align*} \pi \end{align*}, so to get the general solution, you need to write \displaystyle \begin{align*} + \pi n \end{align*} where \displaystyle \begin{align*} n \in \mathbf{Z} \end{align*} after \displaystyle \begin{align*} -0.464 \end{align*}.
• October 3rd 2012, 01:32 AM
TWN
Re: How to find the inverse tangent since the calculator is limited
Quote:

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

You started speaking a language I don't understand in the end there.
• October 13th 2012, 10:44 AM
Kyo
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.