## savac Group Title Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. cos θ = − 5/9, sin θ > 0 one year ago one year ago

1. PeterPan Group Title

Okay, let's make that drawing again, though following @hartnn 's advice, I'll do it properly this time ;) DRAW!!! |dw:1360757734426:dw|

2. PeterPan Group Title

3. savac Group Title

yes

4. PeterPan Group Title

So, we have cosθ = -(5/9) We place the 5 and the 9, accordingly... |dw:1360757883210:dw| (Stop me when you don't understand)

5. savac Group Title

i understand

6. PeterPan Group Title

Now, what's the length of this missing side... |dw:1360758005338:dw| (Hint: Pythagorean theorem)

7. savac Group Title

$\sqrt{106}$ right?

8. PeterPan Group Title

Remember, 9 is your hypotenuse When you have a^2 + b^2 = c^2 9 is your c :)

9. mathsmind Group Title

$\cos ^2(\theta)+\sin^2(\theta)=1$

10. mathsmind Group Title

$\sin^2(\theta) = 1-\cos^2(\theta)$

11. savac Group Title

$\sqrt{56}$

12. mathsmind Group Title

$\sin^2(\theta)=(\frac{- 5 }{ 9 })^2 -1$

13. mathsmind Group Title

i prefer the method provided by @PeterPan, because it shows you the inside out

14. PeterPan Group Title

So, we can put sqrt(56) on here...|dw:1360758287438:dw| And you can easily get the other trig functions. Be careful though...

15. PeterPan Group Title

@mathsmind You do need to do this to illustrate the pythagorean identities you posted. Though if you're not allowed to draw, better know the pythagorean (and other) identities by heart!!! :D

16. mathsmind Group Title

yes that is what i said

17. mathsmind Group Title

i said i prefer the other method to know the inside out

18. savac Group Title

we are allowed to draw on the test

19. PeterPan Group Title

@savac REMEMBER THIS |dw:1360758381571:dw|

20. mathsmind Group Title

although the identity was proven using pyth.

21. savac Group Title

whats that?

22. PeterPan Group Title

ACTS!!!! |dw:1360758433801:dw|

23. savac Group Title

ohhhh thats smart

24. mathsmind Group Title

savac PeterPan is doing a great job

25. PeterPan Group Title

@mathsmind Thanks for the kudos! Much appreciated :)

26. PeterPan Group Title

So back to this... |dw:1360758603756:dw| Can you now determine the rest of the trig functions of this theta?

27. savac Group Title

give me a mint

28. savac Group Title

min

29. PeterPan Group Title

:D I was about to say something clever, but you beat me to it :)

30. PeterPan Group Title

REMEMBER In this particular quadrant, only sine (and cosecant) are positive

31. savac Group Title

lol sorry running low on sleep

32. savac Group Title

ok i got sin=$\sqrt{56}$/9 tan=-$\sqrt{56}$/5 csc=9/$\sqrt{56}$ sec=-9/5 cot=-5/$\sqrt{56}$

33. PeterPan Group Title

34. savac Group Title

cos=-5/9

35. PeterPan Group Title

And there you have it :)

36. savac Group Title

that was rright?

37. PeterPan Group Title

Well yeah, unless you want to make it $\huge \sqrt{56}=2\sqrt{14}$

38. savac Group Title

wow i surprised myself. lol thank you very much

39. PeterPan Group Title

Just place that right triangle in the correct quadrant, and you can't go wrong :) You'll notice that the horizontal bit was to the left of the x-axis, so strictly speaking, that's a -5, not a 5 :D

40. savac Group Title

thats what i thought it was

41. hartnn Group Title

actually since theta is in 2nd quadrant, that is its measure is between 90 to 180, the triangle will be , |dw:1360722028091:dw|

42. PeterPan Group Title

Looks more complicated.

43. hartnn Group Title

but the way its solved and answers are correct.

44. hartnn Group Title

sin and cosec will be positive, all other ratios will be negative.

45. PeterPan Group Title

Yay :)

46. hartnn Group Title

if you want to solve using diagram, then what i have drawn must be used . here, its solved using identities, which is altogether different method and doesn't need drawing triangle.

47. PeterPan Group Title

Identities are harder to swallow, and they taste kinda awful too :(