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secondary 4 | A Maths
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anonymous
Anonymous

secondary 4 chevron_right A Maths chevron_right Singapore

Hi I need help for both parts please :)

Date Posted: 4 months ago
Views: 27
J
J
4 months ago
Each time the hour increases by 1 from midnight, the angle between the hour hand's current position and the hour hand if it were still at 12 o clock increases by π/6

(whole circle is 2π radians, divide by 12 since there are 12 divisions on the clock face, one for each hour)


b)

when h = 25, the needle is at 3 o clock.

Using n = π/6, t = 3, k = 25,

h = acos(nt) + k

25 = acos(π/6 x 3) + k
25 = acos(π/2) + k
25 = a(0) + k
k = 25


When needle is at 12midnight,
h = 25 - 10 = 15, and n = 0

So 15 = acos(0t) + 25

15 = a(1) + 25
a = - 10
Eric Nicholas K
Eric Nicholas K
4 months ago
Or to put it in another way for part i, it takes 12 hours for the hour hand to go one whole round and return to its starting position, ready to go for another round.

The period (time taken to complete one cycle) is 12.

So the frequency (number of cycles in 2pi or 360 deg) is 2pi/period = 2pi/12 = pi/6 radians.
J
J
4 months ago
As for why is the formula as such,

Try drawing a right angled triangle with the hour hand being the hypotenuse.
Eric Nicholas K
Eric Nicholas K
4 months ago
That formula makes sense on its own though. It has to start out as cosine and not sine because the hour hand starts from the highest point “12”. Lots of oscillatory motion in physics such as the movement of a pendulum can be modelled by such equations.

This aside, for some reason it appears that this question has some relations with the equations of circles, simply because they are quite related.
J
J
4 months ago
Sadly most students do not realise this and just apply the formula/substitutions to solve the questions
anonymous
Anonymous
4 months ago
Hi thank you to both as well!
J
J
4 months ago
You're welcome!

See 2 Answers

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Charlene
Charlene's answer
2 answers (A Helpful Person)
1st
Still figuring out part (i).
Eric Nicholas K
Eric Nicholas K
4 months ago
Part i is reasoning. Should not be too difficult.
Eric Nicholas K
Eric Nicholas K
4 months ago
The hour hand takes 12 hours to complete one full cycle and return to its starting position.

So, period is 12 hours.

Frequency is 2#/12 = #/6 (# is my pi symbol).
J
J
4 months ago
If you're on an Android phone there's actually the π symbol
Eric Nicholas K
Eric Nicholas K
4 months ago
Sadly mine is not android. My iphone has no functions for powers, pi and many other symbols.
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Charlene
Charlene's answer
2 answers (A Helpful Person)
Hope this helps!
I did this by trial and error.
anonymous
Anonymous
4 months ago
Thanks! :)