Trig Unit Circle applications

[Live4eva_2]

Hi all,

My math is kinda weak but I'm re-attempting a precalculus course .
I was just wondering exactly how the unit circle helps me??

I mean,I can generate it quite easily(from memory,but)...but why not just convert to degrees and enter it into my calculator?

Also,finding angles that generated a tan value is so tedious...any tips?(I haven't even attempted csc,sec and cot yet)

I'm glad I stumbled across these forums!

 

[stewartcs]

I'm not sure if there is one correct answer as to why a unit circle is beneficial, but I always liked it because it helped me to visualize what was going on. Plus, calculators will often give you the wrong answer when using the arctan function so you'll have to know what quadrant you are in.

CS

 

[Live4eva_2]

Well,



I'll get something like this as an answer(this is an arbitrary value):
x = arctan (sqrt(3)/sqrt(2))
I'll find angles resulting in that value from the trig circle and multiply by
(sqrt(3)/sqrt(3)) to rationalise it,then
the period of the tan graph equals the domain of the arctan function(0,pi-I think).
So I'd restrict my answers to that interval...

I just learned this procedure from my textbook,what confuses me though is how in the world did I end up calculating x = arctan in the 1st place??For what purpose?

Also, I remember when I was doing trig in high school I used the CAST diagram to determine which trig values were positive and negative...I really haven't used it in precalculus yet...Is this because only unit circle angles are evaluated?Or am I missing something?

 

[rocomath]

$$y=tanx$$

Taking the inverse ...

$$x=\tan^{-1}x$$

You calculated arctan so that you could find the angle.

Trig is used a lot in Calculus and Physics, it's not like you're learning this and will not be using it again anytime soon.

 

[Live4eva_2]

Luckily I won't be taking physics again.At best, just this precalculus course and linear algebra.(If I pass those then 1st year discrete also).How do you generate that fancy text??

I guess it's difficult to share knowledge with someone like me..it just goes in one ear and out the other...

Anybody know any tasty acronyms to remember trig identities(besides sohcahtoa)?