sinq-cosq
By Anonymous on Tuesday, January 23, 2001 - 01:05 am :
Can somebody please tell me how to graph sinq-cosq

I really don't have a clue how to do it. All the help greatly appreciated. Thanks.

By Tim Martin (Tam31) on Tuesday, January 23, 2001 - 01:27 am :
The trick is to rearrange into the form of a single trig expression. It is possible to write anything of the form Asinq+ Bcosq as Rcos(q+a)

R cos(q+ a) = sinq- cosq

Expanding using the identity cos(A+B)=cosAcosB - sinAsinB:

Rcosqcosa- Rsinqsina = sinq- cosq

Therefore Rsina = -1

Rcosa = -1

Þ tana = 1

Þ a = p/4

Þ Rsin(p/4) = -1

Þ R = -21/2

Putting this together:

sinq- cosq = -21/2 cos(q+ p/4)

Hope that makes some sort of sense, ask if you aren't sure about the reasoning.

Tim

By Anonymous on Tuesday, January 23, 2001 - 07:02 pm :

Thanks, it makes sense now!!!