# Simplifying Trig Products

1. Oct 30, 2007

### rum2563

[SOLVED] Simplifying Trig Products

1. The problem statement, all variables and given/known data
Express the following as a product and simplify.
sin60° + sin20°

2. Relevant equations

3. The attempt at a solution

I don't understand what the question is trying to say. For example, do I convert sin60° and then add. I don't understand. Someone please help.

2. Oct 30, 2007

### Moridin

3. Oct 30, 2007

### rum2563

So, $$\sqrt{3}/2$$ + sin20°
= 1.208

Could this be right?

Last edited: Oct 30, 2007
4. Oct 30, 2007

### Evalesco

Hi rum2563,
I dont think you are required to solve it, you just ned to rewrite it in a different form.
You will need to use a trig identity which converts the sum to a product.
Moridin has pointed you in the right direction with the hint: "sin a + sin b = some product".
Look on the webpage Moridin has provided a link to and the equation you need is located under Sum-to-Product Formulas.

5. Oct 30, 2007

### rum2563

Thanks Evalesco.

So, here it is:

sin60° + sin20° = 2sin(60+20/2)cos(60+20/2)

Is this right?

Also, because of the fact that you pointed this to me, there is another question I have.

The question states:
Using the method developed in Example 3 (my note: we don't have the book so we don't know what this method is) of this section, prove each of the following Transformation Formulas.

sinx - siny = 2cos(x+y/2)sin(x-y/2)

6. Oct 30, 2007

### Moridin

Not quite; apply the correct formula under the headline "Sum-to-Product Formulas" and do not forget the signs or what should be divided with two.

7. Oct 30, 2007

### rum2563

8. Oct 30, 2007

### Evalesco

Yep it's correct.
Did you mean sinx - siny = 2cos((x+y)/2)sin((x-y)/2)?

I will start you out on one way of showing the above

Start out with sinx - siny

$$Then \ let \ x=\frac{x+y}{2}+\frac{x-y}{2} \ and \ let \ y=\frac{x+y}{2}-\frac{x-y}{2}$$

You will find the identities sin(a+b) = sin(a)cos(b)+cos(a)sin(b) and sin(a-b) = sin(a)cos(b)-cos(a)sin(b) will come in handy for the next step.

Let me know how you get on.

9. Oct 31, 2007

### rum2563

Yes, I finally got it.

sin60° + sin20° = 2sin((x+y)/2)cos((x-y)/2)

A + B = 60°
A - B = 20°
---------- +
2A = 80°
A = 40°

A + B = 60°
A - B = 20°
---------- -
2B = 40°
B = 20°

sin60° + sin20° = 2sin(40°)cos(20°)

Yes, I finally got it. But could there have been an easier way? Or is this good enough? I tried my best anyways.

Thanks to Evalesco and Moridin for helping me out.