Home » 國際課程 » A-level課程 » Details

AQA A Level Maths: Pure復(fù)習(xí)筆記9.1.2 Parametric Equations - Eliminating the Parameter

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日下午12:00

Parametric Equations - Eliminating the Parameter

What does eliminating the parameter mean?

9.1.2-Notes-para_cart

In parametric equations,?x = f(t)?and?y = g(t)
There is still a connection directly linking?x?and?y
- This will be the?Cartesian?equation of the graph

How do I find the Cartesian equation from parametric equations?

9.1.2-Notes-elim_t

STEP 1: Rearrange one of the equations to make t the subject
- Either?t = p(x)?or?t = q(y)
STEP 2: Substitute into the other equation
STEP 3 Rearrange into the desired (Cartesian) form

How do I eliminate t when trig is involved?

9.1.2-Notes-elim_trig_t

STEP 1? Rearrange both equations into the forms “cos t = …” and “sin t = …”
STEP 2? Square BOTH sides of BOTH equations
STEP 3? Add the equations together
STEP 4? The trig identity “sin²?x + cos²?x?≡?1” eliminates?t
STEP 5? Rearrange into desired (Cartesian) form
- This technique is seen in Trigonometric Identities

Exam Tip

When choosing which equation to rearrange, aim for “as simple as possible”:

Linear equations are simpler than quadratics
- eg Rearrange?x = 2t + 3or
  y = 3t²?+3t -4??
Single exponential terms are quite easy to deal with
- eg?x = e^t?→?t = ln x

Trig identities may be needed and remember?squared?terms are good!

eg?sin²?x + cos²?x?≡?1

Worked Example

9.1.2-Example-soltn

轉(zhuǎn)載自savemyexams

以上就是關(guān)于【AQA A Level Maths: Pure復(fù)習(xí)筆記9.1.2 Parametric Equations - Eliminating the Parameter】的解答，如需了解學(xué)校/賽事/課程動(dòng)態(tài)，可至翰林教育官網(wǎng)獲取更多信息。

2026 AMC10/12美國數(shù)學(xué)競賽新賽季！【翰林教育 × 清華大學(xué)出版社】獨(dú)家教材全面發(fā)售！