How would I find the exact value using a sum or difference identity?
2007-10-26 12:51:32 · 4 answers · asked by roguetrader12002 4 in Science & Mathematics ➔ Mathematics
You can do this by using
cos(x+y) = cos(x) cos(y) -sin(x) sin(y)
105 = 60 +45
we know cos and sin of these angles
cos60 =1/2
cos 45 = {sqrt(2)}/2
sin60 = {sqrt(3)}/2
sin45 = {sqrt(2)}/2
cos(60 +45) = cos(60) cos(45) - sin(60) sin(45)
cos(60+45) = (1/2){sqrt(2)}/2 - [{sqrt(3)}/2]{sqrt(2)}/2
cos(60+45) = {sqrt(2)/4} - {sqrt(6)}/4 =
{sqrt(2) -sqrt(6)}/4
Cos (105) = {sqrt(2) -sqrt(6)}/4
2007-10-26 12:57:27 · answer #1 · answered by Anonymous · 1⤊ 0⤋
105 = 60 + 45.
cos (a + b) = (cos a)(cos b) - (sin a)(sin b)
cos 105 = (cos 60)(cos 45) - (sin 60)(sin 45)
cos 105 = (1 / 2)(â2 / 2) - (â3 / 2)(â2 / 2)
cos 105 = â2 / 4 - â6 / 4 = (â2 - â6) / 4.
2007-10-26 12:57:47 · answer #2 · answered by Louise 5 · 2⤊ 0⤋
â cos(105) =cos(90+15) = -sin(15) =-sin(30/2) =
=-â((1-cos30)/2), cos30 = 0.5â3;
2007-10-26 13:05:30 · answer #3 · answered by Anonymous · 0⤊ 0⤋
cos(105) = cos(60+45)
= cos(60)cos(45) -sin(60)sin(45)
2007-10-26 12:59:43 · answer #4 · answered by norman 7 · 1⤊ 0⤋