## anonymous one year ago Determine the sign of sin five pi divided by four without using a calculator.

1. welshfella

|dw:1435357223930:dw|

2. anonymous

Can you explain to me how to find that? @welshfella :)

3. welshfella

what is the sign of opposite / hypotenuse from the diagram

4. welshfella

positive angles go anticlockwise one half a rev is pi and 5pi/4 is another p/4 the signs of the lines are marked

5. welshfella

sin 5pi/4 = - / + = -

6. anonymous

Both hypotenuse and opposite are negative.

7. welshfella

No hypotenuse is always positive

8. anonymous

Oops! I was looking at the wrong part. That was the adj.

9. welshfella

yes the tangent is positive -/- in 3rd quadrant

10. anonymous

"positive angles go anticlockwise" what do you mean by this?

11. anonymous

So the answer would be negative, right? But can you explain to me the steps how to find it? I'm so confused right now. Like what do I need to do first?

12. welshfella

they are measured in an anticlockwise direction angles measured in clockwise direction are negative - that the convention 5pi/4 is equivalent to -3pi/4

13. anonymous

$\sin \frac{ 5 \pi }{ 4 }=\sin \left( \pi+\frac{ \pi }{ 4 } \right)=-\sin \frac{ \pi }{ 4 }=-\frac{ 1 }{ \sqrt{2} }$

14. welshfella

well i've done it using the unit circle . You can also use identities to do these just as surjithayer has just done.

15. welshfella

the 1 / sqrt2 comes from the standard triangle |dw:1435358195274:dw|

16. anonymous

@surjithayer How did you get $-\sin \pi/4?$

17. welshfella

sin pi/4 = 1/sqrt2 therefor - sin pi/4 = -1/sqrt2

18. anonymous

$\sin \left( \pi+\beta \right)=-\sin \beta$ sin is negative in 3rd quadrant.

19. anonymous

Thanks for the help! @surjithayer @welshfella . I'm still kinda confused, but I think I get it now. :)

20. welshfella

yw

21. anonymous

$\sin \left( \pi+x \right)=\sin \pi \cos x+\cos \pi \sin x$ $\sin \pi=0,\cos \pi=-1$

22. welshfella

its just a personal thing but I find it easier to use diagrams for this type of problem

23. anonymous

@welshfella maybe to visualize the problem? Both ways suit for me though. :)

24. welshfella

that s good

25. anonymous

If I change sin five pi divided by four to, let's say, $\tan \frac{5\pi }{ 4 }$, what will be the answer? I just want to practice haha.

26. anonymous

Will it be positive?

27. anonymous

yes it is in 3rd quadrant

28. anonymous

Okay, so can I also assume that cos 5pi/4 is negative based on the All Students Take Calculus?

29. anonymous

yes

30. anonymous

in 3rd quadrant only tan and cot are positive.

31. anonymous

Yes, since cot is just the reciprocal of tan. :)