Pythgorean Identity

[Soconfusedkid]

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

CosC/sinC = - radical 15

Cos^2C/Sin^2C=15

and then (sinC)(-radical15)=cosC

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


Thanks!!

[stapel_eliz]

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:

. . . . .

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]

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]

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]

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

[stapel_eliz]

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.