輔助角

--------------------(16)--------------------

rsin(θ+α)=r[sinθcosα+cosθsinα]

=rcosαsinθ+rsinαcosθ

代入rcosα=a & rsinα=b

=asinθ+bcosθ

考慮sin²α+cos²α=1

r²sin²α+r²cos²α=r²

(rsinα)²+(rcosα)²=r²

(b²+a²)^(1/2)=r

∴r=(a²+b²)^(1/2)

考慮sinα/cosα=tanα

(rsinα)/(rcosα)=tanα

tanα=b/a

∴α=tan^-1b/a

∴asinθ+bcosθ=(a²+b²)^(1/2)sin[θ+tan^-1(b/a)]

--------------------(17)--------------------

rcos(θ-α)=r[cosθcosα+sinθsinα]

=rsinαsinθ+rcosαcosθ

代入rsinα=a & rcosα=b

=asinθ+bcosθ

考慮sin²α+cos²α=1

r²sin²α+r²cos²α=r²

(rsinα)²+(rcosα)²=r²

∴r=(a²+b²)^(1/2)

考慮sinα/cosα=tanα

(rsinα)/(rcosα)=tanα

tanα=a/b

∴α=tan^-1a/b

∴asinθ+bcosθ=(a²+b²)^(1/2)cos[θ-tan^-1(a/b)]