Another trig question (graph) (1 Viewer)

[YBK]

Could anyone please help me out on this one:

Write cosx - sinx in the form Rcos(x+b) where R>0, 0<b<90


Well, i could do this part

(1/R^2) + (1/R^2) = 1

R= root 2 (don't know how to do root sign)

root 2 cos (x +45)

I could do that part, but the next part asked\:

Hence sketch the graph y= cosx - sinx, 0 < x < 360, marking the intercepts on the axis and marking on the axes the y and x values at the turning points.


Alright, I know that the y intercept is 1.
The maximum and minimum points are root2 and - root2
x intercepts are 45, 225

but when it comes to finding x when y = root 2 i get stuck

i get something like this after replacing y with root 2 to get the x value when y is root 2

root 2 = cosx - sinx

How do u solve that?

Thanks again!

Edit: added answer to first part

 

[rama_v]

Could anyone please help me out on this one:

Write cosx - sinx in the form Rcos(x+b) where R>0, 0<b<90


Well, i could do this part

(1/R^2) + (1/R^2) = 1

R= root 2 (don't know how to do root sign)

root 2 cos (x +45)

I could do that part, but the next part asked\:

Hence sketch the graph y= cosx - sinx, 0 < x < 360, marking the intercepts on the axis and marking on the axes the y and x values at the turning points.


Alright, I know that the y intercept is 1.
The maximum and minimum points are root2 and - root2
x intercepts are 45, 225

but when it comes to finding x when y = root 2 i get stuck

i get something like this after replacing y with root 2 to get the x value when y is root 2

root 2 = cosx - sinx

How do u solve that?

Thanks again!

Edit: added answer to first part

the whole point of the transformation into RCos is so that you can solve your question and hence graph it
so anyway it becomes root 2 = root 2 cos (x +45)
1 = cos(x+45)
x + 45 = 0, 360
x = 360 - 45 = 315

 

[YBK]

the whole point of the transformation into RCos is so that you can solve your question and hence graph it
so anyway it becomes root 2 = root 2 cos (x +45)
1 = cos(x+45)
x + 45 = 0, 360
x = 360 - 45 = 315

cool! thanks!!!

much better than what i was trying to do....

can anyone solve root2 = cosx - sinx though?

is there a way to do that?

 

[rama_v]

cool! thanks!!!

much better than what i was trying to do....

can anyone solve root2 = cosx - sinx though?

is there a way to do that?

yes there is, it involves using the t formulae where t = tan (x/2)
Some ppl swear by the t method and will never use the transformation RCos, RSin etc. unless explicitly stated

 

[currysauce]

transformation method > t-method for all real questions hahaha

 

[YBK]

yes there is, it involves using the t formulae where t = tan (x/2)
Some ppl swear by the t method and will never use the transformation RCos, RSin etc. unless explicitly stated

ohh.. yeah, i remember

i'll try that!

Do u think they could actually ask that though?