Ok, I'm having a bad of a time understanding identities for my pre-calc class...all of trig is hard for me to grasp since this is the first time learning any of it (didn't take trig in high school), so basically my question is with subtraction and addition identities. Say I have a problem that says find the exact value of sin 15 degrees and I break it up with sin (x + y) = sinxsiny + cosxcosy (I think that's the right formula?) so it's sin (45 D + 30 D) = sin45sin30 + cos45cos30...ok that's easy enough but I need to get the exact values for each part to find the final solution and I know for instance that sin45 is square root 2/2 (I think anyways) but how would I find that out without already knowing? If it's relevant, I'm using a 84 SE, thanks.
Nov 8th 2006, 10:54 PM
Originally Posted by premedtim
I know for instance that sin45 is square root 2/2 (I think anyways) but how would I find that out without already knowing? If it's relevant, I'm using a 84 SE, thanks.
You should know that 45 degrees is the angle in an equilateral right triangle, and that the sine of an angle in a right triangle is the side opposite the angle divided by the hypotenuse (that’s the longest side).
In the case of an equilateral right triangle we apply Pythagoras's theorem to get the length of the longest side as sqrt(2)s, where s is the length of one of the other sides.
So sin(45) = cos(45) = s/(sqrt(2)s)=1/sqrt(2)=sqrt(2)/2.
You should also know that if you take an equilateral triangle and cut it into
two congruent right triangles you have two 30, 60, 90 degree angle triangles
with sides 1/2, 1, sqrt(3)/2 times the side of the original equilateral triangle.
Which should be enough to allow you to deduce that sin(30)=1/2, and