# Finding sin(7.5)

1. Nov 8, 2007

### rum2563

[SOLVED] Finding sin(7.5)

1. The problem statement, all variables and given/known data
Find sin(7.5) using $$sin\frac{x}{2} = \sqrt{(\frac{1 - cosx}{2})}$$

2. Relevant equations
sin2x = 2sinxcosx
cos(x-y) = coxcosy + sinxsiny

3. The attempt at a solution

$$sin\frac{15}{2} = \sqrt{(\frac{1 - cos15}{2})}$$

= $$\sqrt{(\frac{1 - cos(45-30)}{2})}$$

= $$\sqrt{(\frac{1 - (\frac{\sqrt(2)+\sqrt(6)}{4})}{2})}$$

After this I don't know what to do. I would like some help please. Thanks.

2. Nov 8, 2007

### Avodyne

I think you're done (assuming 7.5 means 7.5 degrees, not 7.5 radians). Unless you want to plug it into a calculator and get a number.

3. Nov 8, 2007

### rum2563

$$\frac{5 + \sqrt{5}}{8}}$$

or

$$\frac{5 - \sqrt{5}}{8}}$$

So I am really confused as to how to get 8 as the denominator. Please help. Thanks.

(Note: 7.5 is degrees.)

Last edited: Nov 8, 2007
4. Nov 8, 2007

### Dick

You don't want to get those answers. They are wrong. And how can there be two of them? You are right.

5. Nov 8, 2007

### rum2563

Yea, I think there must be a typo on the answer sheet. Anyways, thanks to both Dick and Avodyne for analyzing the problem.