p1 trignometry doubttt urgent

[1357913579]

here are the questions

 

[XPFMember]

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!

 

[1357913579]

so can you solve for me these

 

[destined007]

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

 

[destined007]

use these to solve the questions.

 

[1357913579]

do we have to memorize that or is there any sort of concept

 

[destined007]

just memorize. You will learn its concepts in P3. Leave them for now.

 

[Nikesh]

Use the graphs of sin, cos and tan to know the periodic fucntions.
You will be more clear about that.