Trigonometric Identities
Oh joy. Oh yes. It’s another awful maths post, so feel free just to skip right over this. I only type these things up because it’s actually really good revision. It actively encourages me to think about the maths, and I’m likely to see it again when I log in. So without further adue:
Basic Functions:
y=sinx y=cosx y=tanx
cosecx=1/sinx secx=1/cosx cotx=1/tanx
P1 Identities
-
sinA/cosA = tanA
-
cos^2A + sin^2A = 1
P2 Extensions
Divide 2) by cos^2A
- 1 + tan^2A = sec^2A
Divide 3) by sin^2A
- cot^2A + 1 = cosec^2A
Further Identities
- sin(A + - B) = sinAcosB + - sinBcosA
When A = B:
-
sin2A = 2sinAcosA
-
cos(A + - B) = cosAcosB - + sinAsinB (note the change of signs)
When A = B:
- cos2A = cos^2A - sin^2A
Replace -sin^2A with cos^2 - 1:
- cos2A = 2cos^2A - 1
Replace cos^2A with 1 - sin^2A
-
cos2A = 1 - 2sin^2A
-
tan(A + - B) = (tanA + - tanB)/(1 - + tanAtanB) (note the sign orders)
-
sin^2.1/2A = 1/2(1 - cosA)
-
cos^2.1/2A = 1/2(1 + cosA)
Okay, and believe it or not, that’s not everything ;_; - but I have to go to work now, so I’ll finish up later…