Solving Nasty R Equations: Tips & Solutions

[thomas49th]

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 :)

 

[Dick]

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.

 

[thomas49th]

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

 

[HallsofIvy]

Where is the maximum point of sin(theta)? Where is x+ pi/3 equal to that theta?

Same thing for the minimum.

 

[thomas49th]

well sin moves between -1 and 1, so the maximum is when y = 2 and -2 for minimum?
Right?
Thanks

 

[Defennder]

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?