# Thread: Finding trig functions given constraints

1. ## 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: $\displaystyle tan \theta$ is undefined
Constraints: $\displaystyle \pi \le \theta \le 2\pi$

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

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

Am I on the right track? Could anyone also point me in the right direction?

2. ## 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).

3. ## Re: Finding trig functions given constraints

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.

4. ## 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.

5. ## Re: Finding trig functions given constraints

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 $\displaystyle tan \theta = \frac{opp}{adj} = \frac{y}{x}$ undefined.
x = 0 and y = -1 .
I then proceded to solve the functions

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

6. ## Re: Finding trig functions given constraints

Looks pretty good.

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