Question 920910: Suppose cos t = -0.4 and csc t < 0 . Find each of the following
sin t =
tan t =
csc t =
sec t =
cot t =
Is there a way to find this using the unit circle? I am thinking I could draw a right triangle in the 4th quadrant and somehow figure it out from there but i'm not sure. I think the y is negative because csc=1/y which is stated as <0 and therefore negative.
Please explain
Thanks!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Suppose cos t = -0.4 and csc t < 0 . Find each of the following
sin t =-√21/5
tan t =sin/cos=-√21/-2=√21/2
csc t =-5/√21=-5√21/21
sec t =-5/2
cot t =2/√21=2√21/2
Is there a way to find this using the unit circle? I am thinking I could draw a right triangle in the 4th quadrant and somehow figure it out from there but i'm not sure. I think the y is negative because csc=1/y which is stated as <0 and therefore negative.
***
Yes, you could use the unit circle to solve given problem:
First, you must determine which quadrant you are working in. In this case, given data shows you are working in quadrant III where cos<0, sin<0.
y represents the sin function
x represents the cos function
x^2+y^2=1
y^2=1-x^2
x=cos t=-4/10=-2/5
y^2=1-x^2=1-4/25=21/25
y=±√21/25=-√21/5=sin t
coordinates on the unit circle(-2/5,-√21/5)(Quadrant III)
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