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secondary 4 | A Maths

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Hi I need help for both parts please :)

(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

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.

Try drawing a right angled triangle with the hour hand being the hypotenuse.

This aside, for some reason it appears that this question has some relations with the equations of circles, simply because they are quite related.

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So, period is 12 hours.

Frequency is 2#/12 = #/6 (# is my pi symbol).

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I did this by trial and error.