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C3 addition formulas watch

1. How would you solve 3sin(x+10)= 4cos(x-10)??? Between 0<x< 360°
So far I have:
3sinx•cos10°+ 3sin10°•cosx= 4cosx•cos10°+sinx•sin10°
Then finding the actual numbers for cos10 etc but im stuck after that
Thanks ☺️👏🏼
2. (Original post by Shayhay)
How would you solve 3sin(x+10)= 4cos(x-10)??? Between 0<x< 360°
So far I have:
3sinx•cos10°+ 3sin10°•cosx= 4cosx•cos10°+sinx•sin10°
Then finding the actual numbers for cos10 etc but im stuck after that
Thanks ☺️👏🏼
I think you've left something out? When you've corrected it what about collecting like terms?
3. (Original post by Muttley79)
I think you've left something out? When you've corrected it what about collecting like terms?
Ah, the 4cos10°??? (Forgot to type it) And yeah, I've collected like terms before and it didn't get me the answer. Unless I messed up along the way. I'll give it another shot
4. Im doing C3 too, are you supposed to only use 3sin on the sin terms? and 4cos respectively in the expansion? I feel like it should all be multiplied by the number in front, rather than only certain terms.

Nevermind I understand properly now :P

Going to have a go myself.
5. Ok, I get 43.1, 223 degrees. If you move both sinx and cosx to either side and factorise you should be able to rearrange and use an identity to form tanx.

Correct me if I'm wrong though - think i am :P

Hmm, i thought I had committed a heinous division crime but doesn't look like i have.
6. (Original post by Sourestdeeds)
Ok, I get 43.1, 223 degrees. If you move both sinx and cosx to either side and factorise you should be able to rearrange and use an identity to form tanx.

Correct me if I'm wrong though - think i am :P
I wrote the answers down from the book and apparently it's 56.5 and 236.5 >~<
7. Spoiler:
Show
3(sinx * cos10 + sin10 * cosx) = 4(cosx * cos10 + sinx * sin10)
expand and divide by cos 10
3tanx*cos10 + 3sin10 = 4cos10 + 4tanx*sin10
3tanx*cos10 - 4tanx*sin10 = 4cos10 - 3sin10
tanx = (4cos10 - 3sin10) / (3cos10 - 4sin10)
tanx = 1.5126...
x = 56.53, 236.53
voila
8. (Original post by the_sheikh98)
3(sinx * cos10 + sin10 * cosx) = 4(cosx * cos10 + sinx * sin10)
expand and divide by cos 10
3tanx*cos10 + 3sin10 = 4cos10 + 4tanx*sin10
3tanx*cos10 - 4tanx*sin10 = 4cos10 - 3sin10
tanx = (4cos10 - 3sin10) / (3cos10 - 4sin10)
tanx = 1.5126...
x = 56.53, 236.53
voila
Reported for posting full solution - this is not allowed ...
9. (Original post by Muttley79)
Reported for posting full solution - this is not allowed ...
ooh la di da we got a badass over here get over yourself
10. (Original post by 雷尼克)
ooh la di da we got a badass over here get over yourself
It doesn't help if you give a full answer ...
11. (Original post by Muttley79)
It doesn't help if you give a full answer ...
yes it does, even more likely if you're at A-level... an A2 student isn't going to just eat the answer like they did at GCSE, chances are they'll probably go through it... and its especially helpful because trigonometry in C3 can be quite tough - particularly in the regard of knowing what to do... because there are so many formulas.
12. (Original post by 雷尼克)
yes it does, even more likely if you're at A-level... an A2 student isn't going to just eat the answer like they did at GCSE, chances are they'll probably go through it... and its especially helpful because trigonometry in C3 can be quite tough - particularly in the regard of knowing what to do... because there are so many formulas.
It is a rule on this forum that we don't gve the full solution just a hint - like I did. If you think you know better than TSR then petition for a change ... people learn through getting stuck.
13. Sorry, I had a sign error. I get the same answer now
14. (Original post by Muttley79)
It is a rule on this forum that we don't gve the full solution just a hint - like I did. If you think you know better than TSR then petition for a change ... people learn through getting stuck.
You're correct that full solutions aren't supposed to be given unless it is a last resort. However, I highly doubt that the member in question would have realized this, as they are new to the site and may not have read/known the forum specific rules.
15. (Original post by the_sheikh98)
3(sinx * cos10 + sin10 * cosx) = 4(cosx * cos10 + sinx * sin10)
expand and divide by cos 10
3tanx*cos10 + 3sin10 = 4cos10 + 4tanx*sin10
3tanx*cos10 - 4tanx*sin10 = 4cos10 - 3sin10
tanx = (4cos10 - 3sin10) / (3cos10 - 4sin10)
tanx = 1.5126...
x = 56.53, 236.53
voila
despite whatever commotion is going on, thank you very much! I wasn't getting anywhere. Very much appreciated!!

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