Doctor Jolly
. Per Aspera Ad Astra *
There are just some things that I don't get:
1. Find the exact value of 2cos105° sin105°
answer: -1/2
2. Show that sin²7Θ - sin²4Θ = sin11Θsin3Θ
In the answers for this, I understood everything up until the bolded bit:
RHS:
= sin11Θsin3Θ
= sin(7Θ+4Θ)sin(7Θ-4Θ)
= sin²7Θ - sin²4Θ - cos²7Θsin²4Θ
= sin²7Θ(1-sin²4Θ) - (1 - sin²7Θ)sin²4Θ -- how did the take sin²7Θ out of sin²4Θ to make sin²7Θ(1-sin²4Θ)?
= sin²7Θ - sin²7Θsin²4Θ - sin²4Θ + sin²7Θsin²4Θ
= sin²7Θ - sin²4Θ
= LHS
3. Find the number of arrangements of the letters in the word TUESDAY if there are exactly three letters between A and E.
answer: 720
Also, can anyone explain to me when you would use the permutation formula? In all the permutation exercises I've done, I haven't used it, yet I got the answers right ...
4. See attached image:
Sorry if this seems like a lot, but it's just an accumulation of things I didn't get over the past week![Frown :( :(](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Thanks for any help!
1. Find the exact value of 2cos105° sin105°
answer: -1/2
2. Show that sin²7Θ - sin²4Θ = sin11Θsin3Θ
In the answers for this, I understood everything up until the bolded bit:
RHS:
= sin11Θsin3Θ
= sin(7Θ+4Θ)sin(7Θ-4Θ)
= sin²7Θ - sin²4Θ - cos²7Θsin²4Θ
= sin²7Θ(1-sin²4Θ) - (1 - sin²7Θ)sin²4Θ -- how did the take sin²7Θ out of sin²4Θ to make sin²7Θ(1-sin²4Θ)?
= sin²7Θ - sin²7Θsin²4Θ - sin²4Θ + sin²7Θsin²4Θ
= sin²7Θ - sin²4Θ
= LHS
3. Find the number of arrangements of the letters in the word TUESDAY if there are exactly three letters between A and E.
answer: 720
Also, can anyone explain to me when you would use the permutation formula? In all the permutation exercises I've done, I haven't used it, yet I got the answers right ...
4. See attached image:
![](/proxy.php?image=http%3A%2F%2Fi69.photobucket.com%2Falbums%2Fi78%2FMilkiiful_duckz%2Funtitled-1.jpg&hash=9e647bbfec62b8acda3ddf51f916195c)
Sorry if this seems like a lot, but it's just an accumulation of things I didn't get over the past week
Thanks for any help!