# Quick Math Homework Question

1. Nov 7, 2004

### Elijah the Wood

If sin(x) = 8/17, what would sin(x/2) = ???

I knew how to get 8/17, but i have no idea where to go from here
Would you just times the denominator by 2?

Last edited: Nov 7, 2004
2. Nov 7, 2004

### arildno

Remember that:
$$\sin^{2}\frac{x}{2}=\frac{1-\cos(x)}{2}$$
Since:
$$\sin^{2}x+\cos^{2}x=1$$
we have, in this particular case:
$$\cos^{2}x=1-(\frac{8}{17})^{2}=(\frac{15}{17})^{2}$$
Or:
$$\cos(x)=\pm\frac{15}{17}$$
Hence,
$$\sin(\frac{x}{2})=\sqrt{\frac{17\pm15}{34}}$$

You need therefore the SIGN of cosine to determine your value completely.

3. Nov 7, 2004

### brewnog

Solve sin(x) = 8/17 for x
Halve x, then put it back into sin.

4. Nov 7, 2004

### Elijah the Wood

since sin(x/2)=root17+-15/34 would the final answer be sin (x/2)=root+-16/17?

side note: why is sin2x not equal to 2sinx? Is it because in sin2x you are doubling the angle and in 2sinx you're doubling the whole answer?

5. Nov 7, 2004

### arildno

side note: why is sin2x not equal to 2sinx? Is it because in sin2x you are doubling the angle and in 2sinx you're doubling the whole answer?

Doubling the angle does not, in general double the value of the sin.
This is because sin(x) is a NON-linear function of the argument.

$$\sin(\frac{x}{2})=\sqrt{\frac{16}{17}}$$
$$\sin(\frac{x}{2})=\sqrt{\frac{1}{17}}$$