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?

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).

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.

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.

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 $\displaystyle tan \theta = \frac{opp}{adj} = \frac{y}{x}$ undefined.

x = 0 and y = -1 . (Happy)

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

:cool:

Re: Finding trig functions given constraints