Colin James Physics - Mathematics data.

Mathematics icon (fzmaths.jpg).

Last updated: 25th June 2013.

Greek alphabet.
Integrals - Algebraic functions.
Integrals - Hyperbolic functions.
Integrals - Trigonometrical functions.
Series and sequences.
Trigonometry.
Vector algebra (laws).

Trigonometry.

Contents of this page.
Contents icon (fzbooks.jpg).
Trigonometric identities.
Compound angle formulae.
Double angle formulae.
The sine rule.

Trigonometric identities.

cos2q + sin2q = 1

tanq = sinq/cosq
provided cosq ¹ 0

cos(-q) = cosq
sin(-q) = -sinq

sin(p + q) = -sinq
sin(p - q) = sinq

sin(p/2 + q) = cosq
sin(p/2 - q) = cosq

cos(p + q) = -cosq
cos(p - q) = -cosq

cos(p/2 + q) = -sinq
cos(p/2 - q) = sinq

Compound angle formulae.

sin(a + b) = sina cosb + cosa sinb
sin(a - b) = sina cosb - cosa sinb

cos(a + b) = cosa cosb - sina sinb
cos(a - b) = cosa cosb + sina sinb

tan(a + b) = (tana + tanb)/(1 - tana tanb)
provided a + b ¹ ((2n + 1)p)/2

tan(a - b) = (tana - tanb)/(1 + tana tanb)
provided a - b ¹ ((2n + 1)p)/2

Double angle formulae.

sin2a = 2sina cosa

cos2a = cos2a - sin2a
cos2a = 1 - 2sin2a
cos2a = 2cos2a - 1

tan2a = (2tana)/(1 - tan2a)

The sine rule.

Trigonometry icon (fztrig.jpg).

If a, b and c are the lengths of the sides in a triangle and A, B and C are the sizes of the angles respectively opposite these sides then:

a/sinA = b/sinB = c/sinC

End of page.