Posted by **Anonymous** on Monday, April 27, 2009 at 6:06pm.

determine the exact value for sin[cos^-1(4/5)] if XE [0,2pi]

- trig -
**Reiny**, Monday, April 27, 2009 at 6:12pm
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, right-angled 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**, Monday, April 27, 2009 at 6:15pm
OK great! thank you so much

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