STEP question, I don't know what it is asking

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Discussion Overview

The discussion revolves around a STEP (Sixth Term Examination Paper) question, specifically focusing on the interpretation of a problem statement and the mathematical manipulations required to solve it. Participants are seeking clarification on the meaning of certain instructions and how to apply substitutions in the context of integrals and trigonometric functions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the last sentence of the question and requests clarification without being told what to do.
  • Another participant suggests making substitutions and solving integrals on the right-hand side (RHS) to derive equations involving sin(t) and cos(t).
  • There is a request for clarification on which specific sentence is causing confusion, with a mention of calculator restrictions in the exam context.
  • A participant questions how to make the necessary substitutions for f(t) and f(x) and expresses difficulty in equating the expressions.
  • Another participant attempts to guide the original poster on how to relate two equations and solve for coefficients A and B, suggesting differentiation as a method.
  • One participant points out that the equations appear identical and expresses skepticism about the direction of the solution, indicating that differentiation would not yield new insights.
  • There is a challenge regarding the approach to differentiation, with a request for clarification on the derivative being considered.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the interpretation of the problem or the correct approach to take. Multiple competing views and methods are presented, and the discussion remains unresolved.

Contextual Notes

Participants express uncertainty regarding the application of substitutions and the implications of the problem's instructions. There are unresolved mathematical steps and dependencies on the definitions of the functions involved.

Venomily
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question 5.

I am stuck on the last sentence. Please don't tell me what to do, just what they mean.
 

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What equation do you get if you make the substitutions suggested? Can you solve the integrals on the RHS? Having solved them, you will have expressions involving sin(t) and cos(t) on both sides. Treat this as two equations, one involving only the sin terms and one involving only the cos terms.
 
Which sentence are you confused about?

Electronic calculators are not permitted? This just means you can't bring a calculator to use, you must use pencil and paper and the math tables they provide.

or are you talking about problem 13.

EDIT: Oops missed the Question 5 reference. Disregard my response...
 
Last edited:
haruspex said:
What equation do you get if you make the substitutions suggested? Can you solve the integrals on the RHS? Having solved them, you will have expressions involving sin(t) and cos(t) on both sides. Treat this as two equations, one involving only the sin terms and one involving only the cos terms.

I don't know what equation I'll get. How do I make the substitution?

"Use the expression (**) to find A and B by substituting for f(t) and f(x) in (*) and equating coefficients of sint and cost".

@Bolded, just what? :bugeye: how can i possibly 'substitute' f(t) and f(x) into (*)? if it means I set the expressions equal: [*] = [**] this doesn't yield anything.
 
Last edited:
jedishrfu said:
Which sentence are you confused about?

Electronic calculators are not permitted? This just means you can't bring a calculator to use, you must use pencil and paper and the math tables they provide.

or are you talking about problem 13.

I said it at the top of the OP: question 5 :smile:.
 
Basically, your second equation -- related to (**) -- into your first equation -- related to (*).

So, you need to solve for A and B in this equation:

Asin(t)+Bsin(t) = ∫(0->pi) [f(x) sin(x+t)]dxShould be relatively simple. Just take the derivative of each side with respect to x, or you can parse out the integral of f(x)sin(x+t)... I would chose the first choice.

Edit: don't forget that A and B both have f(x) components if you try and take the derivative of the substituted equation.
 
johnkubik said:
Basically, your second equation -- related to (**) -- into your first equation -- related to (*).

So, you need to solve for A and B in this equation:

Asin(t)+Bsin(t) = ∫(0->pi) [f(x) sin(x+t)]dxShould be relatively simple. Just take the derivative of each side with respect to x, or you can parse out the integral of f(x)sin(x+t)... I would chose the first choice.

Edit: don't forget that A and B both have f(x) components if you try and take the derivative of the substituted equation.

I really don't see where this is going, both equations are identical:

sin(t).A+cos(t).B = ∫(0->pi) [f(x) sin(x+t)]dxThis is the same thing as:sin(t).∫(0->pi)[f(x)cos(x)]dx +cos(t).∫(0->pi)[f(x)sinx]dx = ∫(0->pi) [f(x) sin(x+t)]dx

If I tried to differentiate I would just get:

sin(t)f(x)cos(x) dx + cos(t)f(x)sin(x) dx = f(x)sin(x+t) dx

You can't do anything with this equation.
 
I think you are approaching the derivative wrong.
 
johnkubik said:
I think you are approaching the derivative wrong.

please show me what you think the derivative should be.
 

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