Trig Identities
HA cosx/2
+- square root 1 + cosx/2
Half-Angle sinx/2
+- square root 1 - cos/2
HA tanx/2
+- square root 1 - cosx / 1 + cosx 1 - cosx / sinx sinx / 1 + cosx
O/E cot(-x)
-cotx
O/E csc(-x)
-cscx
Odd/Even sin(-x)
-sinx
O/E tan(-x)
-tanx
Reciprocal for secx
1/cosx
Reciprocal tanx
1/cotx
Reciprocal for sinx
1/cscx
Reciprocal for cosx
1/secx
Reciprocal for cscx
1/sinx
Reciprocal for cotx
1/tanx
Double Angle sin2x
2sinxcosx
DA tan2x
2tanx / 1 - tan2x
Sum and Difference cos
cos(x + y) = cosxcosy - sinxsiny cos(x - y) = cosxcosy + sinxsiny
DA cos2x
cos2x - sin2x 1 - 2sin2x 2cos2x - 1
O/E cos(-x)
cosx
Quotient for cotx
cosx/sinx
O/E sec(-x)
secx
S/D sin
sin(x + y) = sinxcosy + cosxsiny sin(x - y) = sinxcosy - cosxsiny
Pythagorean
sin2x + cos2x = 1 tan2x + 1 = sec2x cot2x + 1 = csc2x
Power Reducing
sin2x = 1 - cos2x/2 cos2x = 1 + cos2x/2 tan2x = 1 - cos2x / 1 + cos2x
Sum to Product
sinx + siny = 2sin (x+y/2) cos(x-y/2) sinx - siny = 2cos (x+y/2) sin(x-y/2) cosx + cosy = 2cos (x+y/2) cos(x-y/2) cosx + cosy = -2sin (x+y/2) sin(x-y/2)
Cofunction
sinx = cos(pi/2 - x) cosx = sin(pi/2 - x) tanx = cot(pi/2 - x) cotx = tan(pi/2 - x) secx = csc(pi/2 - x) cscx = sec(pi/2 - x)
Quotient for tanx
sinx/cosx
Product to Sum
sinxsiny = 1/2 [cos(x - y) - cos(x + y)] cosxcosy = 1/2 [cos(x - y) + cos(x + y)] sinxcosy = 1/2 [sin(x + y) + sin(x - y)] cosxcosy = 1/2 [sin(x + y) - sin(x - y)]
S/D tan
tan(x + y) = tanx + tany / 1 + tanxtany