## lilsis76 2 years ago how can i determine which of the two trigonometric values is larger in a, b, and c ? a) cos pi/12 or sin pi/12 b) cos 18 degrees or cos 54 degrees c) cos 320 degrees or sin 290 degrees

1. ChmE

look up the unit circle

2. ChmE

for cos. The higher the degree up to 90 the lower the value. from 90 to 180 the value increases. for sin it is the opposite. **UNIT CIRCLE**

3. lilsis76

okay. im checking it out

4. lilsis76

|dw:1355083613247:dw|

5. lilsis76

okay, well for a) it says cos pi/12 and sin pi/12, how will i know where the pi/12 is??

6. lilsis76

|dw:1355083788207:dw| @ChmE

7. ChmE

its half of pi/6

8. ChmE

cos is the x value and sin in the y value

9. ChmE

you can see the the y value increases to 90 then goes back down. x value it opposite

10. lilsis76

oh...okay i didnt see that. so then the cos would be larger because its sqrt3/2 ?

11. ChmE

|dw:1355084128293:dw|x value is greater than the y value right. more right than up. so cos pi/12 is bigger

12. ChmE

correct

13. ChmE

so what is b)

14. lilsis76

cool, i didnt understand this what so ever last time. let me try the next one okay. and ill give u my answer. could u tell me if its right? so cos 18, would be larger than cos 54 right?

15. ChmE

right

16. ChmE

try C :D

17. lilsis76

okay let me see

18. ChmE

Careful because it is kind of a trick question

19. lilsis76

it be 320?

20. lilsis76

WAIT!, wait y

21. lilsis76

haha y

22. ChmE

yes. because sin is negative in this quadrant. It is a big red flag

23. ChmE

sin will always be less in quadrant 4

24. lilsis76

okay, so the sin would mean its smaller so that means the cos will be smaller too

25. ChmE

I wouldn't say that

26. lilsis76

okay thank you so much haha. im trying to correct my last test givin back to me and i got alot wrong cuz i didnt understand lots of things

27. ChmE

I hope this helped. Just think of cos as the x value on the circle and sin as the y value on the circle. Always helped me