Solving Nasty R Equations: Tips & Solutions

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Homework Help Overview

The discussion revolves around transforming the equation of a curve, specifically y = sqrt3cosx + sinx, into the form y = RSin(x+a), where R and a are constants. The participants are exploring the implications of this transformation and its associated properties.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the initial transformation of the equation and the constants involved. There are attempts to derive the values of R and a, with some participants expressing discomfort with the problem type. Questions arise regarding how to find maximum and minimum points of the graph once the transformation is achieved.

Discussion Status

Some participants have successfully identified values for R and a, while others are exploring how to determine the maximum and minimum points of the graph. Guidance has been offered regarding the relationship between the sine function and its maximum and minimum values, but no consensus has been reached on the specific coordinates of these points.

Contextual Notes

Participants express a general unease with the problem type, indicating a preference for more guidance. There is a focus on understanding the transformation and its implications rather than solving for specific values directly.

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Homework Statement


The curve:
y = sqrt3cosx + sinx

a) Express the equation of the curve in the form y = RSin(x+a), where R and a are constants, R > 0 and 0 < a < pi/2


Homework Equations





The Attempt at a Solution



I don't like these nasty R ones. Can someone walk me through please, point me in the right direction and give me tips :) Thanks :)
 
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I don't like them much either, which is why I don't want you walk you through it. Start by expanding sin(x+a)=sin(x)cos(a)+cos(x)sin(a) and equate the two sides.
 
well i got it

R = 2 and a = pi/3

so

y = 2Sin(x + pi/3)

How do i find:

i) maxiumum point of the graph?
ii) minium point of the graph?
Thanks
 
Where is the maximum point of sin(theta)? Where is x+ pi/3 equal to that theta?

Same thing for the minimum.
 
well sin moves between -1 and 1, so the maximum is when y = 2 and -2 for minimum?
Right?
Thanks
 
Yes, that's right.
Do you want to find maximum values of y or the x-coordinate corresponding to the minima or maxima of y?
 

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