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

1) sinA/cosA = tanA

2) cos^2A + sin^2A = 1

P2 Extensions

Divide 2) by cos^2A

3) 1 + tan^2A = sec^2A

Divide 3) by sin^2A

4) cot^2A + 1 = cosec^2A

Further Identities

5) sin(A + - B) = sinAcosB + - sinBcosA

When A = B:

6) sin2A = 2sinAcosA

7) cos(A + - B) = cosAcosB - + sinAsinB (note the change of signs)

When A = B:

8) cos2A = cos^2A - sin^2A

Replace -sin^2A with cos^2 - 1:

9) cos2A = 2cos^2A - 1

Replace cos^2A with 1 - sin^2A

10) cos2A = 1 - 2sin^2A

11) tan(A + - B) = (tanA + - tanB)/(1 - + tanAtanB) (note the sign orders)

12) sin^2.1/2A = 1/2(1 - cosA)

13) 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…

Go on, read more related posts!

• ‘The Barley Method’
• And so half term approaches…

Filed under: English, Livejournal (old) by Mike on Sunday, February 22nd 2004 @ 5:46 pm | Trackback |