Trigonometry: compound angles

[ the 6 compound angle identities ][ double angle form. ]

[ factor formulae ][ rcos() function ]




The Six Compound Angle Identities


the 6 compound angle identies


back to top


Double Angle Formulae


double angle formulae

back to top


Factor Formulae


the factor fomulae

back to top


rcos() form

Adding a sine and a cosine will generate a cosine curve. This will have a larger amplitude than the original and is out of phase with it.

Writing the expression as rcos(θ - α),

'r' amplitude
'α' no. degrees phase difference(to the right)

Thus expressions of the form:

acos theta plus bsin theta

can be rewritten as

rcos theta plus alpha

Finding 'r' and the phase angle 'α'

rcos form proof




back to top


your stop for the best in math, science & programming tutorials on the Net revision help to get a better result incremental success advanced physics for secondary/high school, including much in-depth content common to first year university courses your one stop for the best in math, science and programming tuition revision help for a better result incremental success advanced physics for high school/secondary and 1st year university fast-track learning for everyone



parametric differen.
equation of a tangent
equation of a normal
rate of change prob.1
rate of change prob.2
the Chain Rule
Chain Rule probs. #1
Chain Rule probs. #2
Chain Rule probs. #3
the Product Rule
parametric eqs.prob#1
parametric eqs.prob#2
intro. to integration
integration by parts 1
integration by parts 2
area under a curve
volumes of revolution
area between curves
Binomial Theorem
Bin. Theorem problems
Trig. Identities
Half Angle Formula
Double Angle Formula
Vector problems
Vector problems in 3D
MORE . . .


derivative formula
tangents & normals
inverse functions
MORE . . .


Edxl C1 Pure specimen
Edxl C1 Pure answers
Edxl C2 Pure specimen
Edxl C2 Pure answers
Edxl C3 Pure specimen
Edxl C3 Pure answers
Edxl C4 Pure specimen
Edxl C4 Pure answers
MORE . . .


the derivative formula
tangents & normals
maxima & minima
chain rule
diffn.trigonometric fns.
product rule
quotient rule
parametric equations
implicit equations
differential equations
integration formula
int.'by substitution'
int.'by parts'
algebraic fractions
definite integrals
areas under curves
volumes of revolution
Trapezium Rule
integ. diff. equations
sine, cosine, tangent
sec, cosec, cotan
Sine & Cosine Rules
Pythagorean ID's
compound angles
Sigma Notation
arithmetic progression
geometic progression
line between points
more straight lines
parametric equations
circles & ellipses
MORE . . .