general solutions (1 Viewer)

[tacogym27101990]

hey can someone show me how to find the general solutions of sin x + cos x =1?
i got x= npi and x=2npi +/- pi/2

but the answer in x=2npi and x=2npi + pi/2

thanks

 

[YannY]

hey can someone show me how to find the general solutions of sin x + cos x =1?
i got x= npi and x=2npi +/- pi/2

but the answer in x=2npi and x=2npi + pi/2

thanks

assuming n is 1, and taking 2npi-pi/2 as a solution. i.e 2pi-pi/2 = 3pi/2
you would have this as a solution but answers would not.
sub back in, sin3pi/2=-1 and cos3pi/2=0
therefore it is not a solution and hence you are mistaken.

i got sin x + cos x = 1
rt2cos(x-pi/4)=1 [Using auxillary angles]
x-pi/4=2npi+/-pi/4
therefore x=2npi and x=2npi+pi/2 [by separating the +/- ]

 

[tacogym27101990]

o yeah
thanks
i'd also tried that but with sine instead of cos

cheers mate