00:01
Today we are looking at number 49, which states that for the following exercises, find the exact value.
00:07
So we are tasked with finding the exact value of sine of 11 pi over 12.
00:13
And to do this, i'm going to choose to use the sum trigonometric identity, which states that sine of u plus v is equal to sine of u times times cosine of v plus.
00:32
Cosine of u times sine of v so basically we need to find two values that add up to 11 pi over 12 from this unit circle and so to do that i've decided to use pi over 4 plus 2 pi over 3 and this ends up being 11 pi over 12.
01:00
I'll show you y over in the side.
01:02
So 3 over 3 times pi over 4 is equal to 3 pi over 12.
01:12
And 4 over 4 times 2 pi over 3 is equal to 8 pi over 12.
01:20
We add these together and we get 11 pi over 12.
01:24
And that's why that we can use these two values.
01:28
And so i'm going to assign 1 .1.
01:30
As u and one as v so pi over four is going to be our u 2 pi over 3 is going to be our v now we just plug and shrug everything into the formula so now we need to find sign of pi over 4 times the cosine of 2 pi over 3 plus cosine of pi over 4 times sine of 2 pi over 4 times sine of 2 pi over 4 times sine of 2 pi over three.
02:08
And now we pretty much just plug everything in...