trig question (1 Viewer)

[DuhBoyChong]

i) Express cosx-sinx in the form Rcos(x+alpha)

ii) Hence solve cosx-sinx=1 for 0≤x≤360

Thank you guys. can't seem to get it.

 

[photastic]

i) R = sqrt(1^2+1^2) = sqrt(2)
alpha = arctan(1) = 45
Therefore cosx - sinx = sqrt(2)cos(x + 45)

ii) cosx-sinx=1
sqrt(2)cos(x + 45) = 1
cos(x + 45) = 1/sqrt(2)
x + 45 = arcos(1/sqrt(2))
x + 45 = 45 , 315
x = 0, 270 , 360

 

[DuhBoyChong]

hey i was wondering why 45 isn't negative and isn't cos 45 1/sqrt(2)

 

[photastic]

Refer to part i where 45 is positive, I've fixed my solution