Thread: Need help with cotangent and tangent functions

1. Need help with cotangent and tangent functions

Okay, I'm attempting to teach myself Trigonometry, but it's very difficult without a teacher. Could anybody tell me how to graph Tangent functions, and then Cotangent functions? I have the general form of a tangent in my notes, but my calculator doesn't want to cooperate with me. ie: One question I have is "Identify the location of the asymptotes of the function: f(theta)=5cot((3/2)theta-(pi/4))+1"

According to the general form of a tangent, the Period should be |pi/b|, which is pi/(3/2) in this problem. But when I type it into my calculator(TI-83 Plus), it gives me 2.094395102. Now how am I supposed to graph that? Also, this calculator won't let me convert from decimal to fraction for some reason, so I don't know what to do. :/

If anybody can help me with this, I will love them forever. Lol.

2. Re: Need help with cotangent and tangent functions

Originally Posted by AngusBelrot
Okay, I'm attempting to teach myself Trigonometry, but it's very difficult without a teacher. Could anybody tell me how to graph Tangent functions, and then Cotangent functions? I have the general form of a tangent in my notes, but my calculator doesn't want to cooperate with me. ie: One question I have is "Identify the location of the asymptotes of the function: f(theta)=5cot((3/2)theta-(pi/4))+1"

According to the general form of a tangent, the Period should be |pi/b|, which is pi/(3/2) in this problem. But when I type it into my calculator(TI-83 Plus), it gives me 2.094395102. Now how am I supposed to graph that? Also, this calculator won't let me convert from decimal to fraction for some reason, so I don't know what to do. :/

If anybody can help me with this, I will love them forever. Lol.
Remember that \displaystyle \begin{align*} \cot{\theta} \equiv \frac{1}{\tan{\theta}} \end{align*}, so in your "Y=" menu, you should type in \displaystyle \begin{align*} Y_1 = 5/ \left(\tan{\left(3 \cdot x / 2 - \pi / 4\right)}\right) + 1 \end{align*}, then press "Graph". You might also need to adjust your window.

3. Re: Need help with cotangent and tangent functions

Originally Posted by Prove It
Remember that \displaystyle \begin{align*} \cot{\theta} \equiv \frac{1}{\tan{\theta}} \end{align*}, so in your "Y=" menu, you should type in \displaystyle \begin{align*} Y_1 = 5/ \left(\tan{\left(3 \cdot x / 2 - \pi / 4\right)}\right) + 1 \end{align*}, then press "Graph". You might also need to adjust your window.
Why would you put a "5/" at the beginning of the equation? Wouldn't you just type the entire equation in parenthesis, and then press the inverse (x-1) key at the end to get the cotangent?

4. Re: Need help with cotangent and tangent functions

yes, you can type it in to a TI this way, also ...

$Y_1 = 5\tan\left(\frac{3x}{2} + \frac{\pi}{4}\right)^{-1} + 1$

Prove it's method is just as valid, and as easy.

5. Re: Need help with cotangent and tangent functions

Originally Posted by AngusBelrot
Why would you put a "5/" at the beginning of the equation? Wouldn't you just type the entire equation in parenthesis, and then press the inverse (x-1) key at the end to get the cotangent?
Maybe because \displaystyle \begin{align*} 5\cot{\theta} \equiv 5\left(\frac{1}{\tan{\theta}}\right) \equiv \frac{5}{\tan{\theta}} \end{align*}.