Question

PLEASE PLEASE HELP THANK YOU
If P(x1) and P(x2) are points in quadrant II on the terminal side of the angles x1 and x2, respectively, with
cos(x1) = − 1/5 and sin(x2) = 2/5, find
sin(x1 + x2), cos(x1 + x2), sin(x1 − x2), and cos(x1 − x2).

Answer 1

LET'S TRY CONSTRUCTING THAT DIAGRAM FIRST

Answer 2

WHICH IS QUADRANT II

Answer 3

the top left

Answer 4

HMM LET ME THINK ABOUT THIS TERMINAL SIDE THING WHAT IT MEANS

Answer 5

EH FORGET THE DIAGRAM WE CAN DO THIS DIRECTLY
WE JUST NEED TO KNOW THAT \[\sin (a\pm b)=\sin a \cos b\pm\sin b \cos a\]
and
\[\cos (a+b)=\cos(a)\cos(b)-\sin (a) \cos(b)\\
\cos (a-b)=\cos(a)\cos(b)+\sin (a) \cos(b)\]

Answer 6

this is all you need to do this
a=x1
b=x2
they give you the info you need

Answer 7

but theyre not on the unit circle. I dont understand that part

Answer 8

what is not on the unit circle?

Answer 9

like for instance sin (-1/5)

Answer 10

what are talking about
we have sin(x1)=-1/5
you don't need sin(-1/5)

Answer 11

yeah but I just dont get how to do each opration...

Answer 12

like for sin(x1+x2)...I dont get what I do to get that answer....

Answer 13

i just give the way
i used a and b instead of x1 and x2

Answer 14

but what do you put in for a and b?

Answer 15

you put x1 and x2
you don't need to put values

Answer 16

the values you gonna need to put are for sin(x1)
sin(x2) , cos(x1), cos(x2)

Answer 17

but i just realized they didn't gave you sin(x1) and cos(x2)
they only gave you cos(x1) and sin(x2)
which brings us to what started with we actually need to draw that figure to find them

Answer 18

this should be something that the figure should look like
so by pythagorean we have
the opposite side to x1 = root(25-1)=root(24)
adjacent side to x2=root(25-4)=root(21)
so sin(x1)= root(24)/5
cos(x2)=root(21)/5
now it is complete