## anonymous one year ago what is the sin, cos, tan, csc, sec, and cot of 0 degrees?

1. jim_thompson5910

Do you have a unit circle with you?

2. anonymous

yes

3. jim_thompson5910

ok locate the angle 0 degrees what is the corresponding point on the unit circle?

4. anonymous

1,0 ?

5. jim_thompson5910

use parenthesis but yeah, (1,0)

6. jim_thompson5910

the x coordinate is equal to cos(theta) the y coordinate is equal to sin(theta)

7. jim_thompson5910

so this means cos(0) = 1 and sin(0) = 0

8. anonymous

tan(0)= 0?

9. jim_thompson5910

to compute tan(0) you use this trig identity $\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

10. jim_thompson5910

yeah you'll find that tan(0) = sin(0)/cos(0) = 0/1 = 0

11. jim_thompson5910

for the other three, use the identities listed on page 2 under the "Reciprocal Identities" section http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

12. jim_thompson5910

eg: csc(x) = 1/(sin(x))

13. anonymous

csc(0)= 0?

14. jim_thompson5910

what was sin(0) equal to again?

15. anonymous

0

16. jim_thompson5910

so csc(x) = 1/(sin(x)) csc(0) = 1/(sin(0)) csc(0) = 1/0 csc(0) = UND or NaN UND = undefined NaN = Not a Number

17. jim_thompson5910

1/0 is NOT the same as 0/1 0/1 = 0 1/0 is undefined because you can't have 0 in the denominator

18. anonymous

so i put undefined?

19. jim_thompson5910

yeah

20. jim_thompson5910

for csc(0)

21. anonymous

and for sec i also put undefined

22. jim_thompson5910

why? what was cos(0) ?

23. anonymous

1

24. jim_thompson5910

take the reciprocal of that to find sec(0)

25. jim_thompson5910

another way to view why csc(0) was undefined is that 0 doesn't have a reciprocal however, sec(0) is defined

26. anonymous

1?

27. jim_thompson5910

yeah sec(0) = 1

28. anonymous

cot(0)= undefined?

29. jim_thompson5910

why?

30. anonymous

tan(0)=0

31. jim_thompson5910

good, and taking the reciprocal of 0 leads to undefined

32. jim_thompson5910

so to summarize sin(0) = 0 cos(0) = 1 tan(0) = 0 csc(0) = und sec(0) = 1 cot(0) = und

33. anonymous

thanks.

34. jim_thompson5910

np