Find the value of trigonometry

1. Dec 7, 2013

songoku

1. The problem statement, all variables and given/known data
Find the exact value of cos 247o+sin 293o

2. Relevant equations
trigonometry identities

3. The attempt at a solution
The furthest I can get is:

cos 247o+sin 293o
= cos 247o - cos 23o
= -2 sin 135o sin 112o
= -√2 cos 22o

Then stuck....

2. Dec 7, 2013

tiny-tim

hi independent!
erm … 203 ?

hint: always subtract from 360° (if necessary), to get an angle less than 180° !

3. Dec 7, 2013

Staff: Mentor

247 = 270 - 23

293 = 270 + 23

cos (270 - 23) = ?
sin (270 + 23) = ?

4. Dec 8, 2013

songoku

Hi independent?? :rofl:

Sorry I don't think I get your hint. cos 23o = - cos 203o. So
cos 247o + cos 203o
= 2 cos 225ocos 22o
= -√2 cos 22o

cos (270 - 23) = - sin 23o
sin (270 + 23) = - cos 23o

So:
- sin 23o - cos 23o
= - sin 23o - sin 67o
= -2 sin 45o cos 22o
= - √2 cos 22o

All lead to - √2 cos 22o. Maybe it is me doing it the wrong way but I don't know how to manipulate the question in other way to give a better result

Thanks

5. Dec 9, 2013

tiny-tim

hi songoku!

ah, i didn't see that
yes, that's the best you can do

(btw, i'd have done cos247 + sin293 = cos113 - sin67 = -cos67 - sin67 = -√2cos22 …

Chestermiller's way of course is also fine, but i'm not as familiar with cos and sin of 270° as he is, so i'd be afraid of making a mistake! )

i'l guess that when the question said "exact", it just meant "compact"

6. Dec 9, 2013

haruspex

Had it said cos 247o+cos 293o there would have been an exact answer. (Note what the two angles add up to.) Misprint perhaps?

7. Dec 10, 2013

songoku

Maybe misprint. Thanks a lot for all the help