C2 Trap Rule

Here is the question
Use the trap rule with four strips each of width 0.25 to find an approx value for (blablabla) where x is in radians. Give your answer to 3 sig fig.

Work it out normally then convert to radians then?
Or just work it out normally and leave it?
Or convert x values to radians and work it out?

Sorry if this is super simple and im being super dumb :frown:

Reply 5

nuodai

Original post by Sockhead

Whenever you do any sort of calculus (differentiation/integration) using trig functions, you should always use radians for everything. I'm not sure what you mean by "work it out normally", but if you're referring to degrees, then you need to change your viewpoint slightly -- you need to get to the point where using radians is "normal" and using degrees is "weird" (which is essentially what happens in A2 and above).

EDIT: just to make this point clear, if you do integration using trig functions without using radians, your answer won't just be in the wrong form, it'll be outright wrong even if you convert things at the end.

(edited 13 years ago)

Reply 6

This is a real problem when people start using radians. They prefer not to use the radians mode at all as degrees seem more familiar and keep converting between the units.

This is a surefire way to come unstuck. Just work in radians all the time unless the question mentions degrees. You will soon get used to it.

Reply 7

lukas1051

No, as long as you are aware you're working in radians, and are aware the numbers you use and maybe the answer will also be in radians.

Radians are just another way of measuring angles, there is nothing special about degrees, as long as you're consistent it will work :smile:

Reply 8

ok. thanks guys :smile:

just to double check, my x values for this particular question would stay at

xo = 0
x1 = 0.25
x2 = 0.5
x3= 0.75
x4 = 1

(lines are x=0 and x=1)
Thanks again

Reply 9

One more fast question :
The equation for this one question is 'cosxdx'
if my d = 0.25 and say x is 1, do i input this into my calculator as cos(1x0.25x1)
Thanks

Reply 10

Original post by Sockhead

One more fast question :
The equation for this one question is 'cosxdx'
if my d = 0.25 and say x is 1, do i input this into my calculator as cos(1x0.25x1)
Thanks

Oh my goodness.

Have you met integration yet? dx is not the product of two quantities d and x.

Reply 11

I know right :frown:

No we haven't got there yet. Our teacher has had too much time off ! Me and a friend were trying to figure out some questions and we haven't been shown trap rule questions with things like cosxdx so we assumed d was the 'distance' ... Sorry

Reply 12

Original post by Sockhead

I know right :frown:

In the context of this question ignore dx altogether. You are trying to find an approximation to the area under the graph y = cos x. If you need more help you need to tell us the number of ordinates or trapeziums you are using and the starting and finishing points (the limits).

Reply 13

Ok. I can differentiate and integrate very simple equations but we havent been shown what to do when a dx or what ever pops up in somthing else.
Here are the questions with dx in them that we are confused about:

1) Use the trapezium rule, with 2 strips each of width 3 to estimate the value for 9 (Long S) 3 log10xdx

2) Use the trapezium rule with 3 strips each of the width 2 to estimate the value of 7 (Long S) 1 Sqrt x^2+3 dx

3) Use the trapezium rule with four strips each of width 0.25 to find an estimate of 1 (Long S) cosxdx where x is in radians.

Reply 14