the subsidiary angle form

First, I list out the format of subsidiary angle form
1. a sinθ+ b cosθ = R sin(θ+α)
2. a sinθ- b cosθ = R sin(θ-α)
3. a cosθ+ b sinθ = R cos(θ-α)
4. a cosθ- b sinθ = R cos(θ+α)

In practice, you ALWAYS ASSUME α to be acute and R > 0, so as to make the transformation easier.

If you don't want to remember these formulae, then you only need to know:

"Subsidiary angle form is DERIVED FROM compound angle formulae."

That is, you can simply expand out the RHS and equate the coefficients of sin x and cos x on both sides
(You don't even remember R = √(a²+b²) and tanα= a/b!!)

你的問題看來只不過是不知
asinθ+bcosθ 如何等於√(a²+b²)cos(θ-α), where tanα=a/b

因
asinθ+bcosθ
=√(a²+b²)[(a/√(a²+b²))(sinθ)+(b/√(a²+b²))(cosθ)]
=√(a²+b²)cos(θ-α)

當中cosα=b/√(a²+b²),sinα=a/√(a²+b²)
則tanα=a/b

條例題中a=√3,b=-1
cosα=-1/2 , sinα=(√3)/2

α一定是第二quadrant﹐因為只有此quadrant sin是+而cos是-

2008-07-03 21:05:52 補充：
其實formula背不背都冇所謂