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P3 Chapters 4 :: �Trigonometry Addition Formula�

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Addition Formulae

 

Do I need to memorise these?

They’re all technically in the formula booklet, but you REALLY want to eventually memorise these.

How to memorise:

First notice that for all of these the first thing on the RHS is the same as the first thing on the LHS!

  • For sin, the operator in the middle is the same as on the LHS.
  • For cos, it’s the opposite.
  • For tan, it’s the same in the numerator, opposite in the denominator.
  • For sin, we mix sin and cos.
  • For cos, we keep the cos’s and sin’s together.

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Common Schoolboy Error

 

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Addition Formulae

 

How to memorise:

First notice that for all of these the first thing on the RHS is the same as the first thing on the LHS!

  • For sin, the operator in the middle is the same as on the LHS.
  • For cos, it’s the opposite.
  • For tan, it’s the same in the numerator, opposite in the denominator.
  • For sin, we mix sin and cos.
  • For cos, we keep the cos’s and sin’s together.

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(Not needed for exam)

 

 

 

 

 

2: We can achieve this by forming two right-angled triangles.

 

3: Then we’re looking for the combined length of these two lines.

 

 

4: We can get the lengths of the top triangle…

 

 

5: Which in turn allows us to find the green and blue lengths.

 

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Proof of other identities

 

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Proof of other identities

 

Bro Exam Tip:

This particular proof came up in 2013 and caught many students off-guard.

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Examples

 

Q

 

 

 

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Exercise 4A/4B and following sums

 

1

a

c

e

2

a

c

e

 

6

3

4

5

 

 

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“That” question

Edexcel June 2013 Q3

 

 

a

b

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Double Angle Formulae

 

Bro Tip: The way I remember what way round these go is that the cos on the RHS is ‘attracted’ to the cos on the LHS, whereas the sin is pushed away.

 

🖉

You will probably never use this 1st form.

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Quickfire Questions

 

 

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Exercises

Exercise 4C

 

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Examples

More prove-y questions:

 

More solve-y questions:

 

 

 

 

 

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More Examples

 

 

 

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Q

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Exercise 4D

Edexcel Jan 2013 Q6

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Q

Bro Tip: I recommend you follow this procedure every time – I’ve tutored students who’ve been taught a ‘shortcut’ (usually skipping Step 1), and they more often than not make a mistake.

 

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Test Your Understanding

 

Q

 

 

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Further Examples

 

Q

 

 

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Bro Tip: This is an exam favourite!

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Quickfire Maxima

 

Expression

Maximum

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Exercise 4E

Part of June 2013 Q8

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Jane 2013 Q4

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‘Factor Formulae’

You already know how to deal with the following:

 

 

 

 

But what about…

 

 

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These are all given in the formula booklet. It’s just a case of knowing how to use them, both forwards and backwards.

‘Factor Formulae’

 

Examples:

 

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Proof

 

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Further Example

 

Hint: combine the first and third term in the numerator and in the denominator (why?).

 

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Exercise 4E/4F