smc-1054-10-Trig

Calculus, EXT2 C1 2023 HSC 15a

Let where is an integer.
Show that for all integers . (3 marks)

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Let where is a positive integer.
By using the substitution , or otherwise,
show that . (4 marks)

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Hence, or otherwise, show that , for all integers . (2 marks)
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i.

ii.

♦♦ Mean mark (ii) 34%.

iii.

♦♦ Mean mark (iii) 28%.

Calculus, EXT2 C1 2020 HSC 16b

Let

Prove that . (3 marks)

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Deduce that . (3 marks)

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Let

Using the result of part (ii), or otherwise, show that . (3 marks)

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Prove that . (2 marks)

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♦ Mean mark (i) 48%.

♦ Mean mark (ii) 36%.

ii.

♦♦♦ Mean mark (iii) 16%.

iii.

♦♦♦ Mean mark (iv) 10%.

iv.

Calculus, EXT2 C1 2002 HSC 2b

For ...

let .

Show that . (1 mark)

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Show that, for ,

. (3 marks)

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ii.

Calculus, EXT2 C1 2008 HSC 3c

For , let .

Show that for ,

. (2 marks)

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Hence, or otherwise, calculate . (2 marks)

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i.

ii.

Calculus, EXT2 C1 2006 HSC 7b

Let , where .

Show that (3 marks)

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Hence find the exact value of

(2 marks)

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STRATEGY: The choice of

and

was extremely important in being able to answer this question. Take note!

i.

$$

ii. $$
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