Question

Cos(85)cos(35)-Sin(85)sin(35)

Answer 1

\(\normalsize\color{blue}{ \cos(a+b)= \cos(a) \cos(b)-\sin(a) \sin(b) }\)

Answer 2

your 'a' is `85`, and your 'b' is `35`

Answer 3

I believe that I would use the trigonometric identity cos(u+or-v)=cosu(cosv)+or-sinu(sinv) @SolomonZelman

Answer 4

That would come out to be cos(85+35)=cos(85)cos(35)-sin(85)sin(35) @SolomonZelman

Answer 5

yes

Answer 6

And re-write \(\normalsize\color{blue}{ \cos(85+35) }\) as \(\normalsize\color{blue}{ \cos(120) }\)

Answer 7

So that would then get me cos(120)=cos(85)cos(35)-sin(85)sin(35). Where do I go from there @SolomonZelman

Answer 8

You can find the exact value of \(\normalsize\color{blue}{ \cos(120) }\)

\(\normalsize\color{blue}{ \cos(120)=\cos(60+60)=\cos(60)\cos(60)-\sin(60)\sin(60) }\)

\(\normalsize\color{blue}{ =\cos^2(60)-\sin^2(60) }\)

Answer 9

\(\normalsize\color{blue}{ \cos^2(60)-\sin^2(60) = (\frac{1}{2})^2- (\frac{\sqrt{3}}{2})^2 =\frac{1}{4} -\frac{3}{4}=-\frac{2}{4}=-\frac{1}{2}}\)

Answer 10

Is that the answer to the problem? @SolomonZelman

Answer 11

yes as exact as I can get.

Answer 12

Thank you very much @SolomonZelman

Answer 13

How would the problem change if it was Cos(85)cos(35)+Sin(85)sin(35) instead of Cos(85)cos(35)-Sin(85)sin(35)? @SolomonZelman

Answer 14

\(\normalsize\color{blue}{ \cos(a±b)= \cos^2(a)∓\sin^2(a)}\)

Answer 15

you tell me

Answer 16

I don't know where to start @SolomonZelman Would the answer be positive instead of negative?

Answer 17

it would be cos(85-35) instead of cos(85+35)

Answer 18

you would get cos(50)

Answer 19

Then what?

Answer 20

then nothing, you can use your calculator to approximate it, but you can't really get an exact answer just like I did by cos(120)

Answer 21

Is this using the sum and difference formula? @SolomonZelman

Answer 22

What is using the sum or difference formula ?

Answer 23

Nevermind, the sum and difference formula is just a trigonometric identity that my teacher wanted me to use when solving this problem. @SolomonZelman I appreciate your help, you have been very thorough and quick with your replies. Have a great day sir!