Solving trigonometric equations using the auxiliary angle method (HSC SSCE Mathematics Extension 1): Flashcards
📚Flashcards
Practise the cards
10 cards from this deck
ShowHide
Practise the cards
10 cards from this deck
What is the auxiliary angle method?
What is the auxiliary angle method?
Rewrite a sin x ± b cos x as r sin(x±α)
How to find α?
How to find α?
tan α = b/a
Convert 3 sin x + 4 cos x to auxiliary form
Convert 3 sin x + 4 cos x to auxiliary form
5 sin(x+α) with tanα = 4/3
General solution for r sin(x+α)=0
General solution for r sin(x+α)=0
x = -α + nπ, n∈Z
Solve 7 sin x - 24 cos x = 0 using auxiliary
Solve 7 sin x - 24 cos x = 0 using auxiliary
r = 25, tanα = -24/7, x = -α + nπ
When to use the auxiliary angle method?
When to use the auxiliary angle method?
When equation has a sin x and b cos x
After transforming a sin x + b cos x = c, next step?
After transforming a sin x + b cos x = c, next step?
Solve r sin(x+α)=c, then use arcsin identities
Example: r for 5 sin x + 12 cos x?
Example: r for 5 sin x + 12 cos x?
r = 13
How to write a sin x + b cos x as one term?
How to write a sin x + b cos x as one term?
r sin(x+α) with tan α = b/a
Auxiliary angle form of a sin x + b cos x?
Auxiliary angle form of a sin x + b cos x?
r sin(x+α), r=√(a^2+b^2), tanα=b/a