# Finding trig functions given constraints

• Jan 25th 2013, 05:11 PM
vaironxxrd
Finding trig functions given constraints
A function value is given along with constraints and I must find all other trig functions based on the given values.

Function value: $tan \theta$ is undefined
Constraints: $\pi \le \theta \le 2\pi$

I can't completely figure out the solution but I've done some work "trying".
First..
$tan \theta = \frac{o}{a} = \frac{y}{x}$ meaning that x is equal to 0. because of the constraints I made an unit circle and assumed theta is $\frac{3\pi}{2}$
Therefore,

$sin \theta$ = ?
$cos\theta$ = ?
$tan\theta$ = undefined
$csc\theta$ = ?
$sec\theta$ = undefined
$cot\theta$ = ?

Am I on the right track? Could anyone also point me in the right direction?
• Jan 25th 2013, 05:23 PM
chiro
Re: Finding trig functions given constraints
Hey vaironxxrd.

Are you just trying to find when the trig functions are undefined? If so then use the fact that tan(theta) = sin(theta)/cos(theta) and put all trig functions into rational functions (like I did with tan) and find when the denominator is equal to 0 (which will mean its undefined there).
• Jan 25th 2013, 06:11 PM
vaironxxrd
Re: Finding trig functions given constraints
Quote:

Originally Posted by chiro
Hey vaironxxrd.

Are you just trying to find when the trig functions are undefined? If so then use the fact that tan(theta) = sin(theta)/cos(theta) and put all trig functions into rational functions (like I did with tan) and find when the denominator is equal to 0 (which will mean its undefined there).

Thank you for the advice Chiro. The question is asking me to find the values of all six trig functions, I assume I must use tan for that (as you said).
I'm just confused if I must make an unit circle and used the x,y,r values or just use an angle value. I feel the question doesn't give enough information for the x,y,r.
• Jan 25th 2013, 07:00 PM
chiro
Re: Finding trig functions given constraints
One suggestion I have is use the fact for a circle, x = rcos(t) and y = rsin(t) for a circle of radius r centered at the origin. Once you solve for t in radians you can plug in the value to get the (x,y) point.
• Jan 26th 2013, 07:26 AM
vaironxxrd
Re: Finding trig functions given constraints
Quote:

Originally Posted by chiro
One suggestion I have is use the fact for a circle, x = rcos(t) and y = rsin(t) for a circle of radius r centered at the origin. Once you solve for t in radians you can plug in the value to get the (x,y) point.

I was able to figure out a method for solving it, hopefully you can correct me on a more efficient way.

Because tan Θ is undefined and the constraints say it must lie between Quadrant 3 or 4, I was able to figure out that theta must be 3pi/2.
The reason is because at angle 3pi/2 x = 0 and therefore making $tan \theta = \frac{opp}{adj} = \frac{y}{x}$ undefined.
x = 0 and y = -1 . (Happy)
I then proceded to solve the functions

sin = $\frac{opp}{hyp}$ = $\frac{y}{r}$ = -1
cos = $\frac{adj}{hyp}$ = $\frac{x}{r}$ = 0
tan = $\frac{opp}{adj}$ = $\frac{y}{x}$ = Undefined
csc = $\frac{hyp}{opp}$ = $\frac{r}{y}$ = -1
sec = $\frac{hyp}{adj}$ = $\frac{r}{x}$ = Undefined
cot = $\frac{adj}{opp}$ = $\frac{x}{y}$ = 0

:cool:
• Jan 26th 2013, 04:21 PM
chiro
Re: Finding trig functions given constraints
Looks pretty good.