Question

If sin a=.25 and cos b=.25 what is sin b/2 + cos a/2?

Answer 1

is 1.604680374

Answer 2

I'm getting 2 ???

Answer 3

probably not????

Answer 4

i'm sorry

Answer 5

0.375

Answer 6

1.343245

Answer 7

answer?

Answer 8

No problem literally this is all GREEK to me!! :D appreciate your help

Answer 9

\[\sin ^{2}\left( \frac{ b }{ 2 } \right) = \frac{ 1 - \cos b }{ 2 }\]and\[\cos ^{2}\left( \frac{ a }{ 2 } \right) = \frac{ 1 + \cos a }{ 2 }\]where\[\cos a = \sqrt{1 - \sin ^{2}a}\]Using that last equation,\[\cos a = \sqrt{1 - (0.25)^{2}} = 0.9682458\]Using this in the second equation\[\cos ^{2}\left( \frac{ a }{ 2 } \right) = \frac{ 1 + 0.9682458 }{ 2 } = 0.9841229\]

Answer 10

The first equation is easy.\[\sin ^{2}\left( \frac{ b }{ 2 } \right) = \frac{ 1 - 0.25 }{ 2 } = 0.375\]So, now you just add the sqrt of this and the sqrt from my previous post.

Answer 11

1.604329687

Answer 12

Yes, that's close enough. I rounded when I gave you some of the partial results from calculations. btw, was this a multiple-choice question?

Answer 13

yes it was thank you so so so much!!!!!!!!!!!!!!!!!!!!!!!!

Answer 14

Well, between Openstudy MathJax not working for me for a while, and my mistake from before, I'm surprised you waited for me!

Answer 15

What did your multiple-choice answers look like exactly? That would be very informative.

Answer 16

Needed your help badly
wrote a comment for you " GOOD ONE!"

Answer 17

1.60 ,1.32,.26,1.06

Answer 18

Ok, that's good. What I was looking for was whether or not the answer contained radical signs and if it didn't, how far it went with the decimal places. It confirms the validity of my method, although I'm going to look at this one for a while and see if there was an easier way. If you don't stick around, I'll message you on what I find.

Answer 19

Thank you wasn't given any formulas to solve from class been looking on internet for trig formula sheets

Answer 20

So Bright makes Sheldon from " Big Bang Theory" look ignorant!!!!!! posted as a testimony for you !! Thanks man

Answer 21

OK! I just went through it all again, and if there is any shorter way, it cannot be much shorter at all. I really think you have to go through all these steps to get the answer, and it's obviously a lot of work. But it's fun! And I just saw your Sheldon comment. It's not true of course, but maybe I should start wearing long sleeves under my t-shirts! :-)

Anyway, this was a lot of fun (for math nerds like me!) And you're wonderful to work with! Thanks for the very nice comments!

Answer 22

Thank you

Answer 23

you are very very welcome! @maltman0004 I had to look at your profile to realize that you are Melissa. Before I did that, I thought you were a guy that likes malts!

Answer 24

lol its my college ID MALTMAN lol last name Altman and 1st initial

Answer 25

In any case, I like malts, I like Sheldon, and I sure like working with you! @maltman0004