anonymous one year ago Given sin (theta) = 21/29... find sin cos and tan (2 theta)

1. Loser66

$$sin(\theta)=\dfrac{opposite}{hypotenuse}$$ how about cos(theta)?

2. anonymous

3. Loser66

ok, let them there. Now, pythagorean |dw:1435110885323:dw| Can you put numbers on the triangle?

4. Loser66

on that triangle, which side is hypotenuse?

5. anonymous

left side is hyp bottom is adj and right side is opp

6. Loser66

you use draw box below, click on it, then a box will pop up. On the right corner, you will see "copy previous drawing", click on it, then scroll up to see my picture, click it to get the pic, then put the numbers in, then post

7. Loser66

|dw:1435111234190:dw|

8. Loser66

hence, the adj side can be calculated by Pythagorean. Do you know him?

9. Loser66

don't get??

10. anonymous

oh a2 + b2 = c2

11. Loser66

Mr. Pythagore said : In this case, $$adj = \sqrt{29^2-21^2}=??$$

12. Loser66

13. Loser66

Don't get or you got the answer?? If you don't answer me, I am out in 2 more minutes.

14. anonymous

gimme one second

15. anonymous

35.8?

16. Loser66

redo.

17. anonymous

wait why is it minus?

18. anonymous

isnt the formula a squared plus b squared equals c squared?

19. Loser66

a^2 +b^2 =c^2, hence a^2 = c^2 -b^2

20. anonymous

ahhhh got it

21. anonymous

so its asking for 2 theta not just theta

22. anonymous

i got that the adj is 20

23. Loser66

yup

24. Loser66

now, you have all of them, plug in cos (theta) = adj/ hyp = ???

25. anonymous

no i get that part but i need to find sin (2 theta) cos (2 thetha) and tan 2 (theta)

26. anonymous

cos(theta) = 20/29

27. Loser66

ok, tell me cos (theta) =??

28. anonymous

20/29

29. Loser66

yup

30. anonymous

now how do i find 2 theta?

31. Loser66

now $$sin(2\theta) = 2 sin(\theta)cos(\theta)$$

32. Loser66

just plug numbers in, right?

33. anonymous

ahh gotcha so cos (theta) = 2cos (0) tan (0)?

34. Loser66

nnnnnnnnnnnnnnnnnoppppppppppe

35. Loser66

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

36. anonymous

what is this called? i feel like i should google these formulas lol

37. Loser66

just type double angle trig formula.

38. Loser66

But, you should memorize some easy formulas.

39. anonymous

got it thank you so much

40. Loser66

ok, and you know tan = sin /cos, right?

41. anonymous

its not 2 tan ( ) / 1 - tan ^2 ( )?

42. Loser66

you have sin (2 theta), cos (2 theta), why don't you use them?

43. Loser66

$$tan (\color{red}{x}) =\dfrac{sin(\color{red}{x})}{cos(\color{red}{x})}$$ $$tan(\color{blue}{2x})=\dfrac{sin(\color{blue}{2x})}{cos(\color{blue}{2x})}$$ got it?

44. anonymous

oh okay makes sense

45. Loser66

good luck. I am out now