Solving for sin(7.5) using half-angle formula

[rum2563]

[SOLVED] Finding sin(7.5)

Homework Statement

Find sin(7.5) using $$sin\frac{x}{2} = \sqrt{(\frac{1 - cosx}{2})}$$

Homework Equations

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

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.

 

[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.

 

[rum2563]

In our answer sheet, the answer for this question is:

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

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.)

 

[Dick]

In our answer sheet, the answer for this question is:

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

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.)

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

 

[rum2563]

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