Question 95528
the circumference of any circle is 2pi radians.
An angle of pi (-1,0)is 180 degrees from the standard position (1,0) on the circumference going counterclockwise.
-pi (-1,0) has the same coordinates but arrives there from the standard position going clockwise.
In the unit circle sin=y cos=x & tan=y/x
In this case sin=0 cos=-1 tan=0/-1=0 csc=1/0=und. sec=1/-1=-1 cot=-1/0=und
We derived all of these above formulas from (-1,0).
Easy, huh!
2nd question:
sin(t)=0.6, cos(t)<0
sin is + in quadrants 1 and 2
cos is <0 (ie. negative) in quadrants 2 and 3
So the terminal side of the angle is in quadrant 2
y=.6
If we draw a right triangle in quadrant 2 using the suppliment of the angle as our reference angle then y=.6 is the opposite side and the hypotenuse=1. In the unit circle the hypotenuse is always 1 and is always positive!
Now we can find x which is negative (quadrant 2).
y^2+x^2=c^2
.36+x^2=1
x^2=1-.36=.64
x=-.8
cos=-.8 tan=-.6/.8=-.75 cot=-.8/.6 csc=1/.6 sec=-1/.8=-1.25
EdJones