OnLine HW Help

[that82toyota]

Hey guys, this is my first calculus course and I seem to understand most of the content so far but something came up in the online HW that we had not covered.

find
Limit sin(⍬)
⍬->(pi/4) ⍬

In other words find the lim as theta approaches pi over 4 of sin(theta) over theta.
I know it looks a little scrunched up.
We have been working with limits for a week or so but I am not to fresh on my trig functions.
Any help is greatly appreciated, THX!!

 

[ksdhart]

Well, limits with trig functions are no different than any other limits. So, the first step is to just try a straight substitution. Sometimes when you do that, the value is undefined, and that means that more advanced techniques (which you probably haven't gotten to yet) may help you find the value. In this case, however, the limit has a finite value.

\(\displaystyle \displaystyle{\lim_{\theta \to \frac{\pi }{4}}\left(\frac{sin\left(\theta \right)}{\theta }\right)=\frac{sin\left(\frac{\pi }{4}\right)}{\frac{\pi }{4}}=\frac{4sin\left(\frac{\pi }{4}\right)}{\pi }}\)

And since \(\displaystyle \frac{\pi }{4}=45°\), the value can easily be calculated. If you haven't already, I strongly recommend you memorize the values of sine and cosine for 0, 30, 45, 60, and 90 degrees. These values will show up a lot.

 

[that82toyota]

Hey thanks much, I worked it after viewing your suggestion and arrived at the correct answer.

 

[Steven G]

Hey guys, this is my first calculus course and I seem to understand most of the content so far but something came up in the online HW that we had not covered.

find
Limit sin(⍬)
⍬->(pi/4) ⍬

In other words find the lim as theta approaches pi over 4 of sin(theta) over theta.
I know it looks a little scrunched up.
We have been working with limits for a week or so but I am not to fresh on my trig functions.
Any help is greatly appreciated, THX!!

You should always direct substitute with limits. The only time you will not be done after substituting is if you have to reduce/simplify or you get 0/0 ( remember this is calculus 1). If you get 0/0 then things could get messy.