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C3 addition formulas

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 ☺️👏🏼

Reply 1

Muttley79

Original post by Shayhay

I think you've left something out? When you've corrected it what about collecting like terms?

Reply 2

Shayhay

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

Reply 3

Sourestdeeds

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.

(edited 8 years ago)

Reply 4

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

Hmm, i thought I had committed a heinous division crime but doesn't look like i have.

(edited 8 years ago)

Reply 5

Shayhay

Original post by Sourestdeeds

I wrote the answers down from the book and apparently it's 56.5 and 236.5 >~<

Spoiler

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 :biggrin:

Reported for posting full solution - this is not allowed ...

Reply 8

雷尼克

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

Reply 9

Muttley79

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 ...

Reply 10

雷尼克

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.

Reply 11

Muttley79

Original post by 雷尼克

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.

Reply 12

Sourestdeeds

Sorry, I had a sign error. I get the same answer now

Reply 13

spotify95

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.