Posted by Soroban on September 09, 2002 at 11:31:55:
In Reply to: Re: Sin & Cos posted by Joel on September 09, 2002 at 00:13:43:
: : 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)
What Joel said is absolutely correct.
Did you follow it?
I would guess from #1 that you are expected to
KNOW the trig values for 30deg, 60deg, and 45deg.
I'm sure they was in a previous lesson.
For a 45deg right triangle, the sides are 1, 1, sqrt(2).
[The hypotenuse is always the longest side.]
From there, you should be able to "build" the
six trig values for 45deg (pi/4).
For a 30-60 right triangle, the sides are, 1, sqrt(3), 2.
I've always said, "One, Two, Square root of three."
(I has a nice rhythm to it.) But I have to remember
that the hypotenuse is 2 (the longest side).
Where do the other numbers go? "1" (the shortest
side) is opposite 30 (the smallest angle).
Now you can work out the trig values for 30deg
and 60deg (pi/6 and pi/3) - without a calculator!
You see, this is a neat way to "carry those
triangles in your head" - ready to use at any time.
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