## Math4Life Find the value of tan (a-b) if cos a = 3/5 , sin = b 5/13, 0° < a < 90°, and 0° < b < 90° one year ago one year ago

1. Math4Life

@hartnn think you could help me on this one? :)

2. hartnn

know the formula for tan(a-b) ??

3. Math4Life

kind of, i'm doing an alternative thing for my teacher where we try to work ahead on stuff we haven't learned yet so I don't really understand the concept, I want the answer because it gives me extra credit, but I want to understand and for you to explain it to me so I know how to do it for the future :)

4. Math4Life

@Callisto @campbell_st @completeidiot

5. campbell_st

you need to find the missing sides in 2 triangles |dw:1357801664006:dw| find x and y using pythagoras' theorem... this should be easy. then find for angle a.... the ratio for tan(a) and for angle b.... the ratio for tan(b) then substitute the ratios into the expansion of tan(a - b) hope this makes sense

6. Math4Life

It kind of makes sense, do you think you could work through the problem with me?

7. campbell_st

ok... what are the lengths of x and y...?

8. Math4Life

well we haven't figured them out yet

9. campbell_st

can you calculate them using pythagoras' theorem $5^2 = 3^2 + x^2$ and $13^2 = 5^2 + y^2$

10. Math4Life

x = 4, -4 y = 12, -12

11. campbell_st

well with mesurements... you can only use the positives... you can show me -3 metres... but you can show me 3 metres ok... next step what is tan(a) = and tan(b) = both answers will be fractions...

12. Math4Life

1.1578 or -1.1578 0.2126 or -0.2126 right?

13. campbell_st

nope not as decimals as fractions... just like in the question cos(a) = 3/5 you need to write them like that

14. campbell_st

and only use positive values...

15. Math4Life

Ok well let me convert them to fractions

16. campbell_st

remember tan = opp/adj|dw:1357802645909:dw|

17. Math4Life

22/19 and 7/33

18. campbell_st

not even close... you said x = 4 and y = 12 so what would tan(a) = and tan (b) =

19. campbell_st

|dw:1357802809114:dw|

20. Math4Life

a as in x and b as in y, correct?

21. campbell_st

use the measurements in the drawing above to write fractions for tan(a) = and tan (b) =

22. Math4Life

I am so confused right now, how do i solve for a and b?

23. campbell_st

ok... do you understand that tan = opposite/adjacent... ?

24. Math4Life

kind of

25. campbell_st

ok... from the diagram below |dw:1357803166503:dw| what is tan(a) = just write a fraction using the side measurements given

26. Math4Life

4/3

27. Math4Life

or 3/5?

28. campbell_st

great tan(a) = 4/3 now for angle b |dw:1357803706601:dw| what is tan(b) = as a fraction

29. Math4Life

12/13?

30. campbell_st

not quite tan = opposite/adjacent so tan(b) = 5/12 ok... do you know the expansion of tan(a - b)....?

31. Math4Life

So tan(4/3 - 5/12) which is 30/23

32. campbell_st

nope start with the expansion $\tan(a - b) = \frac{\tan(a) - \tan(b)}{1 + \tan(a)\tan(b)}$ so substitute tan(a) = 4/3 and tan(b) = 5/12 then just calculate it out...

33. campbell_st

oops it should read $\tan(a - b) =\frac{ \tan(a) - \tan(b)}{1 + \tan(a)\times \tan(b)}$

34. Math4Life

tan(4/3 - 5/12) = tan(4/3) - tan(5/12)/1 + tan(4/3) tan(5/12)

35. campbell_st

nope... just put the fractions in (4/3 - 5/12)/(1 + 4/3 x 5/12)

36. Math4Life

which is 33/35

37. Math4Life

is 33/35 my final answer?

38. Math4Life

Ok i'm not trying to seem pushy but can we hurry it up here? It's 3am here and I have to get up at 5:30am and this is my last problem on my practice test

39. Math4Life

I appreciate all your help and time thank you :)

40. campbell_st

good luck... you really need to know trig basics to be able to do this problem.

41. Math4Life

If I keep working on this with you how long will it take? because I'm extremely tired

42. campbell_st

well your answer is close it should be 33/56

43. Math4Life

Thank you for everything tonight

44. campbell_st

good luck

45. Math4Life

Thank you I appreciate it