1. anonymous

2. jim_thompson5910

hint for the first part $\Large \frac{13\pi}{12} = \frac{\pi+12\pi}{12}$ $\Large \frac{13\pi}{12} = \frac{\pi}{12} + \frac{12\pi}{12}$ $\Large \frac{13\pi}{12} = \frac{\pi}{12} + \pi$

3. anonymous

I'm not sure what it is that they want.. they are asking for the coordinates i'm a little lost :/

4. amistre64

for a unit circle ... x = cos(t) y = sin(t)

5. amistre64

but working them into their radical values might be a bit daunting :/

6. jim_thompson5910

|dw:1444012468609:dw|

7. jim_thompson5910

|dw:1444012481543:dw|

8. jim_thompson5910

|dw:1444012492630:dw|

9. jim_thompson5910

add pi to pi/12 to get 13pi/12 this is the same as doing a 180 degree rotation |dw:1444012532760:dw|

10. jim_thompson5910

compare the two points marked on the unit circle the x coordinates are the same in magnitude, but they differ in sign (the first is positive, the second is negative) same for y coordinates

11. anonymous

that makes sense,.. so when they mention the terminal point p(x,y) how would I determine that?

12. jim_thompson5910

it's essentially point P but the signs are different for each coordinate

13. jim_thompson5910

|dw:1444012707085:dw|

14. jim_thompson5910

$\Large P = \left(\frac{\sqrt{2+\sqrt{3}}}{2}, \frac{\sqrt{2-\sqrt{3}}}{2}\right)$

15. jim_thompson5910

$\Large Q = \left(\color{red}{-}\frac{\sqrt{2+\sqrt{3}}}{2}, \color{red}{-}\frac{\sqrt{2-\sqrt{3}}}{2}\right)$

16. anonymous

so for 13pi/12 the terminal point would be -sqrt2+sqrt3/2?

17. jim_thompson5910

it would be point Q I wrote above

18. anonymous

i'm a little confused :/

19. jim_thompson5910

all I did was take the coordinates of point P and make them negative

20. jim_thompson5910

point P is the point corresponding to pi/12 point Q is the point corresponding to 13pi/12

21. anonymous

so how would I follow this pattern for 5pi/12?

22. jim_thompson5910

Hint for part 2 5pi/12 = (pi + 4pi)/12 5pi/12 = pi/12 + 4pi/12 5pi/12 = pi/12 + pi/3 Then use these identities $\Large \sin(x+y) = \sin(x)\cos(y)+\cos(x)\sin(y)$ $\Large\cos(x+y) = \cos(x)\cos(y)-\sin(x)\sin(y)$

23. anonymous

I'm really lost..

24. jim_thompson5910

I'm guessing you've never seen those identities before?