Posted by Anonymous on .
determine the exact value for sin[cos^1(4/5)] if XE [0,2pi]

trig 
Reiny,
cos^1(4/5)
tells me the angle is in either I or IV, since the cosine is positive in the first and fourth quadrants.
make a sketch in the first quadrant, rightangled triangle with hypotenuse 5 and base of 4 (r=5, x=4)
by Pythagoras the other side is 3, or y=3
so in the first quadrant sin[cos^1(4/5)] = 3/5
and in the fourth quadrant sin[cos^1(4/5)] = 3/5 
trig 
Anonymous,
OK great! thank you so much