Posted by Joel on September 09, 2002 at 00:13:43:
In Reply to: Sin & Cos posted by Mig on September 08, 2002 at 22:54:09:
: Can anyone help w/ this?
: Find the exact value of each expression without using a calculator.
: 1. sin pi/3 cos pi/4 - sin pi/4 cos pi/3
: 2. cos^2 (-270) - sin^2 (-270)
1. Draw 2 right triangles, one with angles pi/3, pi/6, pi/2; the other with pi/4, pi/4, pi/2. (Remember that 360 degrees = 2pi radians.)
You will probably soon realize what the lengths of the sides of those triangles are, and that will tell you the exact values of the sines and cosines you need, in terms of sqrt(3) and sqrt(2).
2. A point rotating in a full circle around the origin covers an arc of 360 degrees, right? Normally we measure angles by beginning at a point on the positive x-axis & rotating counter-clockwise. Think of the point rotating in the opposite direction, clockwise. So an angle of minus 270 degrees is equal to how many degrees in the positive direction? Get that & you will know what the corresponding sine & cosine are.
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