## Pythgorean Identity

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Soconfusedkid
Posts: 3
Joined: Mon Feb 28, 2011 11:33 pm
Contact:

### Pythgorean Identity

Hey guys whats up?
So I have a slight issue i missed a day of school and i have no idea how to solve this problem. Please help me? Show work too please/ explain so it makes sense lol. Thanks

If coT c = - radical 15 and <C is in quadrant IV, find csc C.

I'm lost all i got

Cos^2C/Sin^2C=15

I have no idea if this is even remotely correct please let me know and show what is next?

Thanks!!

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
If coT c = - radical 15 and <C is in quadrant IV, find csc C.
Draw the x,y-plane.

Draw a right triangle in the fourth quadrant, with the triangle "hanging" from the x-axis (that is, with one leg being on the positive x-axis). Label the angle at the origin as "C".

Use what you know about the cotangent ratio to label the two legs of the triangle, noting that the y-value must be negative, and using the fact that:

. . . . .$-\sqrt{15}\, =\, -\frac{\sqrt{15}}{1}$

Then use the Pythagorean Theorem to find the length of the hypotenuse.

Now that you have all three sides labelled, read off the value of the cosecant.

Soconfusedkid
Posts: 3
Joined: Mon Feb 28, 2011 11:33 pm
Contact:

### Re: Pythgorean Identity

I feel really stupid :/ ok so coT is cos/sin so how would I figure out the sides of the triangle? And and -15/1 as the y-value? I'm lost sorry :/

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
I feel really stupid :/ ok so coT is cos/sin so how would I figure out the sides of the triangle?
Hint: SOHCAHTOA
And and -15/1 as the y-value?
Relate the values in the fraction to the sides in the trig ratio to label two sides of the triangle.

Soconfusedkid
Posts: 3
Joined: Mon Feb 28, 2011 11:33 pm
Contact:

### Re: Pythgorean Identity

Awesome Thanks I think I got it.... is the answer 4?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Awesome Thanks I think I got it.... is the answer 4?
Close. But you need to take the signs in the fourth quadrant into account.