## anonymous one year ago Find an exact value. cos 165°

1. Nnesha

whats two number you can add to get 165? and those two number suppose to be on the unit circle

2. Nnesha

then use formula $\large\rm cos(a+b)=\cos a \times \cos b - \sin a \times \sin b$

3. anonymous

90 & 75 ?

4. Nnesha

well 75 is not on the unit circle :/

5. Nnesha

|dw:1438365794651:dw|

6. anonymous

120 + 45

7. Nnesha

30+135 40+120 225-60 for this u have to use cos(a-b)=cos a times cos b + sin a times sin b

8. Nnesha

perfect!

9. Nnesha

so $\huge\rm cos(45+120)=\cos 45 \cos 120 - \sin 45 \sin 120$

10. anonymous

okay, i see. what do i do from there?

11. Nnesha

so $\large\rm cos(45+120)=\cos 45 \cos 120 - \sin 45 \sin 120$ now use the unit circle cor exact value of cos and sin cos 45 =? cos 120 =? sin 45=? sin 120 =? plugin their exact values

12. anonymous

cos 45 = (radical)2 / 2 cos 120 = -1/2 sin 45 = (radical) 2 /2 sin 120 = (radical) 3 /2 is that right?

13. Nnesha

$\frac{ \sqrt{2} }{ 2 } \times \frac{ -1 }{ 2 } - \frac{ \sqrt{2} }{ 2 } \times \frac{ \sqrt{3} }{ 2}$ solve

14. Nnesha

yes that's right