SOLUTION: Can anyone help explain how to do this problem to me please? FInd the exact values of the trigonometric function given that sinu= -12/13 and cosv= 24/25 (Both u and v are in qua

Question 118681: Can anyone help explain how to do this problem to me please?
FInd the exact values of the trigonometric function given that sinu= -12/13 and cosv= 24/25 (Both u and v are in quadrant IV.)
Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
FInd the exact values of the trigonometric function given that sinu= -12/13
sinu = y/r = -12/13
(Both u and v are in quadrant IV.)
-------------------
If u is in the 4th quadrant y = -12 and r = 13
--------
r^2=x^2+y^2
x^2 = r^2-y^2
x^2 = 13^2-(-12)^2
x^2 = 169 -144 = 25
x = 5 in the 4th quadrant
-----------------------
So:
sinu = -12/13
cosu = x/r = 5/13
tanu = y/x = -12/5
cscu = r/y = -13/12
secu = r/x = 13/5
ctnu = x/y = -5/12
-----------------------
and cosv= 24/25
cosv = x/r=24/25
y^2 = r^2-x^2 = 25^2-24^2 = 49
x = 24, y = 7 , r = 25
---------------
sinv = y/r = 7/25
cosv = x/r = 25/25
tanv = y/x = 7/24
etc.
==========
Cheers,
stan H.

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