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    Hey guys.
    Just wondering, when you are given your equation in the question ect and it goes on to say 'x is in radians'
    do I need to convert x to degrees before I work out my y values or what?
    This has be super confused!!

    Ta
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    (Original post by Sockhead)
    Hey guys.
    Just wondering, when you are given your equation in the question ect and it goes on to say 'x is in radians'
    do I need to convert x to degrees before I work out my y values or what?
    This has be super confused!!

    Ta
    Isn't this just telling you to give x in radians for your final answer?
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    If x is in radians, work the whole thing out in radians, and y will be in radians. Only convert back to degrees if it asks for an answer in degrees, and be careful about calculator modes when using sin and cos in the exam.
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    If in doubt, just use radians for everything (unless something's obviously in degrees, e.g. if you see numbers like 30, 45, 60, 90, 135, 180, 225 or 360 kicking around).
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    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
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    (Original post by Sockhead)
    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
    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.
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    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.
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    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
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    ok. thanks guys
    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
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    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
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    (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.
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    I know right 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
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    (Original post by Sockhead)
    I know right 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
    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).
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    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.
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    (Original post by Sockhead)
    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.
    Just ignore the integral sign and the dx in each case.

    First one you need to find the area under the graph y = log x (where log is the logarithm to base 10) between x = 3 and x = 9.

    You need 2 strips (3 ordinates - it is always one more than the number of strips).

    x0 = 3 so y0 = log 3

    x1 = 6 so y1 = log 6

    x2 = 9 so y2 = log 9

    The width of the strips is h=3 (the gap between consecutive ordinates).

    Substitute this information into the formula and you have the answer.
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    Oh I see Missing out dx in all cases seems simple enough to what me and my friend were suggesting to each other!
    Thanks alot
 
 
 
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