## Math4Life Use a half–angle identity to find the exact value of sin 105° one year ago one year ago

1. baziham

i completely answered to you. you must use sin and cos formula and use 105=90+30/2 sin(a+b)=.. sin(2a)=.. cos(2a)=.. try it

2. Math4Life

Ok i'm trying it right now

3. Math4Life

I got -0.260736296 and I have a feeling its not right

4. jim_thompson5910

they want the exact value, not an approximation

5. Math4Life

Yes exact value

6. jim_thompson5910

Hint: Use the half angle formula $\Large \sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1-\cos(\theta)}{2} }$

7. Math4Life

I'm so confused

8. jim_thompson5910

notice how 105 = 210/2

9. Math4Life

and 210/2 is 105

10. Math4Life

so are you saying 210 is my answer?

11. jim_thompson5910

no, I'm saying the fact that 210 (which is an angle found on the unit circle) divided in half gives you 105

12. jim_thompson5910

so sin(105) = sin(210/2)

13. jim_thompson5910

then you would use that formula I gave above

14. jim_thompson5910

I'll get you started Start with this fact $\Large \sin(105) = \sin\left(\frac{210}{2}\right)$ Then use the formula given previously to get $\Large \sin(105) = \sqrt{\frac{1-\cos(210)}{2} }$ Then use the unit circle to evaluate cos(210) and simplify as much as possible

15. Math4Life

Ok I understand

16. baziham

where $\cos(210)=\cos(180+30)=\cos(180)\cos(30)-\sin(180)\sin(30)$

17. baziham

answer is $\sqrt{\frac{ 1-\left\{ \cos(180)\cos(30)-\sin(180)\sin(30) \right\} }{ 2 }}$

18. baziham