Michael J. answered • 04/30/15
Tutor
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Effective High School STEM Tutor & CUNY Math Peer Leader
We need to find two values that give the sum or difference of 255. Let's use values that can we easily find sine and cosine of. The angles we can easily find sine and cosine of are 0, 30, 45, 60, 90, 180, 270, and 360. Then apply the addition or subtraction formula.
sin(225 + 30)
because 225 + 30 = 255.
sin(225)cos(30) + cos(225)sin(30) =
sin(225)(√(3) / 2) + cos(225)(1/2)
Next, we do the same thing to sin(225) since this is not obvious to us. Find two angles that give the sum or difference of 225. Then apply the addition or subtraction formula.
sin(225) = sin(180 + 45)
= sin(180)cos(45) + cos(180)sin(45)
= -√(2) / 2
cos(225) = cos(180 + 45)
= cos(180)cos(45) - sin(180)cos(45)
= -√(2) / 2
Now, we substitute this simplified value of sin(225) into the previous step.
sin(225)(√(3) / 2) + cos(225)(1 / 2) =
(-√(2) / 2)(√(3) / 2) + (-√(2) / 2)(1 / 2) =
(-√(6) / 4) - (√(2) / 4) =
( -√(6) - √(2)) / 4
