## anonymous 5 years ago what is the exact value of sin15 ? (using the subtraction formula)

1. anonymous

help!

2. anonymous

I don't know about the subtraction formula (never heard of it) but the half angle identity should work

3. nikvist

$\sin^215=\frac{1-\cos 30}{2}=\frac{1-\sqrt{3}/2}{2}=\frac{2-\sqrt{3}}{4}$ $\sin15=\frac{\sqrt{2-\sqrt{3}}}{2}$

4. anonymous

That's it right there^

5. anonymous

I think the subtraction formula would mean that you would take two sin values that you know and use them to get sin 15 Sin 45 - Sin 30 I will get back with the formula

6. anonymous

OK here is the formula sin(A−B) = sin A cos B − cos A sin B

7. anonymous

im required to use this formula sin(s-t)= sin(s)cos(t) - cos(s)sin(t)

8. anonymous

Sin(45-30) = sin45*cos30 - cos45*sin30

9. anonymous

Sin 45 = sqrt2/2 cos 45 = sqrt2/2 sin 30 = 1/2 cos 30 = sqrt3/2

10. anonymous

The difference identity! Yup that works better!

11. anonymous

sqrt2/2*sqrt3/2 - sqrt2/2*1/2 sqrt6/2 - sqrt2/2 (sqrt6 - sqrt2) /2

12. anonymous

would it be over 4 after multiplying

13. anonymous

OOPS - yes

14. anonymous

thanks so much!

15. anonymous

U R Welcome