Asymptotes

[Probability]

Any help would be appreciated. I have two very small paragraphs on this subject and the only maths in it says;

tan theta = sin theta / cos theta

asymptote at theta = 90⁰

I have a activity that asks me to write down the values of theta between 360⁰ and 720⁰ at which the asymptote of a tangent graph occurs.

I have no examples of how this is done and as said very limited information to do it, but I have assumed "probably" incorrectly that this could be the way to do it?

360⁰ + 90⁰ = 450⁰
and

720⁰ - 90⁰ = 630⁰

I would of thought that there would have been a more precise mathematical way of doing this, but would appreciate any advice.

Regards

Probability

 

[JeffM]

Any help would be appreciated. I have two very small paragraphs on this subject and the only maths in it says;

tan theta = sin theta / cos theta

asymptote at theta = 90⁰

I have a activity that asks me to write down the values of theta between 360⁰ and 720⁰ at which the asymptote of a tangent graph occurs.

I have no examples of how this is done and as said very limited information to do it, but I have assumed "probably" incorrectly that this could be the way to do it?

360⁰ + 90⁰ = 450⁰
and

720⁰ - 90⁰ = 630⁰

I would of thought that there would have been a more precise mathematical way of doing this, but would appreciate any advice.

Regards

Probability

$\displaystyle Because\ tan(\theta ) = \dfrac{sin(\theta )}{cos(\theta )},\ tan(\theta )\ is\ not\ defined\ whenever\ cos(\theta ) = 0.$

But the cosine function is a periodic function, meaning it repeats regularly. The cosine function is zero at EVERY odd multiple of 90 degrees,
which means the tangent function does not exist at EVERY odd multiple of 90 degrees. (The sine function and tangent function are also periodic.)

And 360 is 4 * 90 and 720 is 8 * 90. So there are only two odd multiples between 4 and 8, namely 5 and 7.

Simple logic. Quite precise. Very well done. Stop doubting yourself.