00:01
So in order for us to answer these two, they actually write the first one, kind of giving us a hint as to how we go about solving it.
00:12
Because if we were to just combine those two, so 315 minus 60 is 255, and i don't know what sign of 255 is.
00:26
But since we have it in this difference, we can use the difference formula for sine.
00:34
And i'll kind of write this right above it.
00:36
So it's sine of u minus v.
00:42
And this is going to be equal to sine of u cosine of v minus then sine of v.
00:53
Cosine of u and so we just plug these in so in this case our u is 315 our b is 60 so this is going to be sine of 315 times cosine of 60 minus sine of 60 cosine of 315 then over here i'll just kind of draw a unit circle really quickly just to kind of orient where all these are so 60 degrees is up top here and then 315 i believe is right here so 315 so at 60 we know cosine is smaller so that's one half we know sign is bigger so that's root 3 over 2 and then at 315 well it's one of the 45s so it's going to be root 2 over 2 for both but the y is going to be negative or sign is going to be negative.
01:59
So this is root 2 minus root 2 over 2.
02:03
And then we just come up here and plug those points in.
02:07
So again, sign of 315 is negative root 2 over 2.
02:11
Cosign of 60 is 1 half minus.
02:15
So sign of 60, root 3 over 2.
02:18
Cosign of 315, root 2 over 2.
02:22
And then we can go ahead and simplify this down...