• We need your support!

    We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
    Click here to Donate Now (View Announcement)

p1 trignometry doubttt urgent

XPFMember

XPRS Moderator
Messages
4,555
Reaction score
13,290
Points
523
Assalamoalaikum!!!

You dont get these type of questions in the exam! But you should know these...you wont be asked to prove them...but u'll need to have knowledge of these to solve questions!
 
Messages
1,148
Reaction score
166
Points
73
The sine and cosine functions are periodic with a period of 360 degrees. This means that sin(x+360)=sin(x) and cos(x+360)=cos(x) or sin(x+2(360))=sinx and cos(x+2(360))=cosx or sin(x+3(360))=sinx and cos(x+3(360))=cosx and so on. However, tan has a period of 180 degrees so tan(x+180) = tanx =tan(x-180)
By observing the graphs of sin and cos, we can express the sin function in terms of cos and vice versa:
sin(x) = cos(90- x)
and the cos function in terms of sin:
cos(x) = sin(90 - x)

you will find that once you draw cos(x) and cos(x+180), the graphs will be mirror images (in the x axis) of each other. The same goes for sin and tan.
Therefore,
cos(x+180)= -cosx
sin(x+180)= -sinx
tan(x+180)= tanx

sin(x) = cos(x - 90)=cos(90-x)
sin(x+90)=cos(x)
cos(x+90)=-sin(x)

here are derivations:
1) sin (90 + x)
sin90 x cosx + cos90 x sinx
1.cosx + 0.sinx
sin(90 + x) = cosx


2) sin(90 - x)
sin90 x cosx - cos90 x sinx
1.cosx - 0.sinx
sin(90 - x) = cosx


3) cos(270 - x)
cos270 x cosx + sin270 x sinx
0.cosx + (-1).sinx
cos(270 - x) = -sinx


4) cos(270 + x)
cos270 x cosx - sin270 x sinx
0.sinx - (-1).sinx
cos(270 + x) = sinx
 
Messages
96
Reaction score
32
Points
28
Use the graphs of sin, cos and tan to know the periodic fucntions.
You will be more clear about that.
 
Top