Question

What's answer of (sin 160 + sin 20) / (cos 140+cos 70)

Answer 1

Are you supposed to use a calculator? Those aren't common unit circle angle measures and I don't see a way to simplify with any identities.... so I think you would just punch it up in your calculator.

Answer 2

I have calculated that (sin 160 + sin 20) is 2 sin 20. But, I am so confused about ((cos 140+cos 70)....

Answer 3

Well, using cos(x)=sin(90-x) we can get that cos(70)=sin(20)

And cos(140)=-cos(40)=-cos(2*20)

So (cos 140+cos 70)=-cos(2*20)+sin(20) so that makes the whole thing:

(sin 160 + sin 20) / (cos 140+cos 70)=2*sin(20)/(sin(20)-cos(2*20))

So that puts everything in terms of 20*.
But I'm still not sure where to go with it after that, if you need an exact numerical evaluation...

Answer 4

I have calculated what your answer above, and I am also confused... DebbieG ...

Answer 5

\[\sin 160 + \sin 20 = 2\sin 90\cos 70\]
\[\cos 140 + \cos 70 = 2\cos 105\cos 35\]

Answer 6

Yes, Mrtsj, thanks beforehand... I have reached what you write, but I am confused to continue it...

Answer 7

Do the directions say to simplify or what?

Answer 8

not simplify, but to calculate the final answer...

Answer 9

http://www.wolframalpha.com/input/?i=%28sin160%2Bsin20%29%2F%28cos140%2Bcos70%29

Answer 10

I am still confused, there isn't the answer what I mean on the website...

Answer 11

Ahhh, I had forgotten about sum-to-product identities. But yeah, I'm still not sure how you could evaluate an exact result here without a calculator. I mean, you can certainly simplify:

\( \dfrac{\sin 160 + \sin 20}{cos 140 + \cos 70 } =\dfrac{ 2\sin 90\cos 70}{2\cos 105\cos 35}=\dfrac{ \cos 70}{\cos 105\cos 35}\)

Hmmmmmm...... now, the only thing I notice about this is that it is of the form:

\( \dfrac{ \cos \alpha}{\cos (\alpha + 45)\cos (\alpha/2)}\)

I have no idea if that's relevant or how it might help, though... lol.

Answer 12

.9933763474? idek..

Answer 13

But i want to calculate it without a calculator....