## anonymous one year ago how does csc(-120) equal to -csc(120)?

1. Nnesha

sin and tan are odd cos = even $\large\rm sin(-\theta)= -\sin \theta$$\large\rm cos(-\theta)= \cos \theta$$\large\rm Tan(-\theta)= - Tan \theta$

2. anonymous

I still don't understand

3. Nnesha

what is reciprocal of sin ,cos and tan ???

4. anonymous

Honestly I have no idea. I am the worst with trigonometry. I don't understand it whatsoever

5. Nnesha

then u need to start it over $\large\rm sin =\frac{ 1 }{ \csc }~~\cos=\frac{ 1 }{ \sec }~~~\tan=\frac{ 1 }{ \cot }=(\frac{ \sin }{ \cos })$ reciprocal of sin is 1/csc reciprocal of cos is 1/sec reciprocal of tan is 1/cost or you can say sin /cos csc=1/sin sec=1/cos cot=1/tan csc , sec and cot are reciprocal of sin , cos and tan

6. Nnesha

if sin =a/b then csc = b/a

7. Nnesha

so if sin is odd function then csc is odd or even ?

8. anonymous

odd

9. Nnesha

yes right that's how $\huge\rm csc(-120)= - \csc(120)$

10. anonymous

another way of looking at it is using the unit circle and fact that neg angle goes clock-wise |dw:1440006652430:dw|

11. anonymous

but I'm just not understanding how the negative comes out

12. anonymous

sin refers to "y-value" , on the circle sin(-120) is the neg y-value of sin(120)

13. anonymous

|dw:1440007033356:dw|

14. anonymous

oooooh okay, i get it more now lol. thank you!

15. anonymous

is this also true for cosine ?

16. Nnesha

cos = odd

17. Nnesha

$\large\rm cos (-45)= \cos(45)$ |dw:1440007938868:dw| x-coordinate represents cos function

18. anonymous

wouldn't the cosine be negative too since it's in the 3rd quadrant ?

19. Nnesha

20. Nnesha

for odd and oven just remember sin(-x)= -sin(x) cos(-x)=cos(x) tan(-x)= -tan(x)

21. Nnesha

@dumbcow

22. anonymous

so it's not true for cos of theta ?

23. Nnesha

yes right cos (-120) = cos(120)

24. Nnesha

cos is even

25. anonymous

how do I prove that ?

26. anonymous

my question says to pick a value of theta and to test the theory

27. Nnesha

i guess because cos is negative in 2nd quadrant and in 3rd quadrant so negative times negative = positive even

28. Nnesha

:P i just know the basic stuff don't know how to explain better than that sorry

29. anonymous

thank you