# Math Help - re:simplifying trig

1. ## re:simplifying trig

Hello.
I am trying to simplify the following -
cos40cos20-sin40sin20
I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.
However, the answer only requires that I give 1/2, and not √3/2?
Thanx

2. Originally Posted by morelemonzanybody?
Hello.
I am trying to simplify the following -
cos40cos20-sin40sin20
I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.
However, the answer only requires that I give 1/2, and not √3/2?
Thanx
$\cos A \cos B - \sin A \sin B = \cos (A+B)$

Hi:
I am aware of the addition formulae.
For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
Is it like this?
cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
This seems awfully long winded to do by hand.
And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?

4. $
sin(90-\theta) = cos(\theta)
$

I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.

sin(60) =√3/2= cos(30)

cos(60) = 1/2 = sin(30)

And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?

Use the above thing to write it in cos()= "xxxxx"

Incase this is not what you are asking please make question a bit clear

well:
I guess what I'm trying to say is that I really don't understand the steps they have taken in the problem. I must be missing the point.
So, do I:
1/ add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
2/ take cos60 to be 1/2, and sin60 to be √3/2
3/ but that means 1/2 - √3/2, which is wrong.

or,
1/ add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
2/ cos60sin30-sin60cos30, which is 1/2 x 1/2 - √3/2 x √3/2 = -1/2
And, why is the answer sin=1/2, and not cos=1/2
I'm really getting confused here

6. Originally Posted by morelemonzanybody?
Hi:
I am aware of the addition formulae.
For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
Is it like this?
cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
This seems awfully long winded to do by hand.
And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?
There are only two steps necessary:

$\cos(40)\cos(20) - \sin(40)\sin(20) = \cos(40+20) = \cos(60)$

Now, look at the attached triangle to find $\cos(60)$

You should find $\cos(60) = \frac{1}{2}$, and that's it! Game over.

7. Originally Posted by morelemonzanybody?
Hi:
I am aware of the addition formulae.
For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
Is it like this?
cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
This seems awfully long winded to do by hand.
And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?
With $\sin(A)\cos(B) + \sin(B)\cos(A)$, you can simplify to $\sin(A+B)$

8. 1 add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
Cos(a) +cos(b) is not equal to cos(a+b)
sin(a)+sin(b) is not equal to sin(a+b)

2 take cos60 to be 1/2, and sin60 to be √3/2
its a fact that cos(60degrees) = 1/2 and sin(60degrees) = √3/2
Don't take it as assumption

3 but that means 1/2 - √3/2, which is wrong.
Yes its wrong!!!!

1 add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.

Cos(a) +cos(b) is not equal to cos(a+b)
sin(a)+sin(b) is not equal to sin(a+b)

2 cos60sin30-sin60cos30, which is 1/2 x 1/2 - √3/2 x √3/2 = -1/2

This has no meaning forget this concept

9. ## re: the game

And a fine Game it was too, Mush.
Arigatogozaimasu

10. ## re: the game

sorry
should have said:
arigatogozaimashita
past tense