maths HELP!

[tredes]

ok i have a question for my maths. Its probly an easy question, but im kinda struggling...

please help

 

[FAST6191]

My usual do not do the whole question rule is in effect.
I assume points A and B only just touch the circle.

Go back to triangles for this one and you will need radians on a calculator.

You have a triangle 10 cm (aka the radius) above point A.

You have one side 7cm long and the other is again the radius (10cm)
Need the angle now.
simple trigonometry gives us this one.
add pi/2 (90 degrees if you are still working in degrees for some reason).

Arc length is explained here:
http://www.themathpage.com/aTrig/arc-length.htm

pi x diameter = circumference (not so important now but you will need it in a minute)

the point on the circle is 2 cm above B in the vertical sense or 8cm below the horizontal radius.
repeat first part to get angle. This time however you have 1.5 times pi (or 270 degrees if again you are still in degrees)

Now you have the angles/lengths and whatever and knowing the diameter of the circle (you do not actually need it but it may help alleviate some of the confusion if you do it that way) you can work out distance travelled fairly easily.

 

[tredes]

should you do the whole question in rads.. or is it possible to jus do it with degrees?? we have jus been introduced to rads and there still a lil bit confusing..

thanks

 

[nintendofreak]

Dont worry radians are just units!!


a complete "rotation" of a circle is "2pi" units (our units will be, radians!). If you divide it up into the 4 quadrants, each quadrant has a value of pi/2 radians!

msg back, i'll be here for a wile before i have to go to schools too!

 

[FAST6191]

This sort of thing (that and calculus with trigonometric functions) is the whole reason radians exist (and I would bet the whole reason you were given this question).

You will need to convert them to use the arc length formula but you could leave them in degrees until you need to actually crunch numbers.

Anyhow you have probably used radians for years and not thought about it/known it as nintendofreak hints at:
the circle circumference is pi x diameter = 2 x pi x radius and as 2 x pi is the full circumference of the circle in radians.......

 

[tredes]

hahaha yehh troo my lecturer was a tool when he gave this sheet...didnt understand shit ey....

but yeh im getting there now..thanks alot guys!!!

 

[gizmo_gal]

Oh My God...I cant do Math beyond Long Multiplication and Long Division....I suck at Algebra...

 

[distorted.freque]

Oh My God...I cant do Math beyond Long Multiplication and Long Division....I suck at Algebra...

I know Algebra and that doesn't look like Algebra. It lacks...variables. Unless Algebra also covers that. O_O

 

[tredes]

im still confused...i dont understand how by working out those arcs will determine the distance travelled...

very confused...

 

[FAST6191]

OK. The thing about circles is each that any point can be used to measure rolling distance because by definition all points are the same distance from the middle of the circle. Convention tends to dictate the point in contact with the floor or the one opposite the floor (think trundle wheel) is used but in this case you are using the given point on the circle.

measure the first arc. Call it 20cm (note not the correct answer by any stretch).
measure the second arc. Call it 50cm.

30cm difference: 30 cm is has been rolled.

Note however you could just use angles and work out a single arc between the two points (this is the "you do not actually need..." it part I was on about earlier) and have it right away.