## anonymous one year ago If sin θ = 12 over 37, use the Pythagorean Identity to find cos θ.

1. Nnesha

Identity is $\huge\rm sin^2 \theta +\cos^2 \theta =1$ substitute sin for 12/37 solve for cos

2. Nnesha

|dw:1440269530637:dw|

3. Nnesha

or you can draw a right triangle ^^^$\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }$

4. anonymous

|dw:1440269641978:dw|

5. anonymous

alright thx. wasn't sure i was solving it right.

6. Nnesha

np :)

7. anonymous

Refer to the attachment.

8. anonymous

cos θ = ± 35 over 37 cos θ = ± 23 over 37 cos θ = ± 35 over 12 cos θ = ± 20 over 35 are my answer choices... little confused now.

9. Nnesha

you need cos theta for right triangle you hve to apply Pythagorean theorem $\huge\rm a^2+b^2=c^2$

10. Nnesha

11. Nnesha

$\huge\rm \sin \theta =\frac{ opposite }{ hyp } =\frac{ 12 }{ 37 }$|dw:1440270658205:dw| find 3rd side of right triangle

12. anonymous

thats where i get lost. do i just substitute each of those in for the variables

13. Nnesha

remember c is the longest side of right triangle (hypotenuse )

14. anonymous

a^2+12^2=37^2... right?

15. Nnesha

yes right!!

16. anonymous

and if i rearrange it to solve for a i get 35^2?

17. Nnesha

hmm not square

18. Nnesha

you would subtract 12^2 both sides or you can take square of 12 first and the subtract it doesn't matter $c^2= \sqrt{37^2-12^2}$

19. anonymous

35

20. Nnesha

yes right

21. anonymous

22. Nnesha

yes right :=)

23. anonymous

thx much

24. anonymous

can you help with one more?

25. Nnesha

i'll try

26. anonymous

What are the sine, cosine, and tangent of 5 pi over 4 radians?

27. anonymous

i can't find the tan

28. Nnesha

$\huge\rm tan \theta =\frac{ \sin \theta }{ \cos \theta }$ :=)

29. Nnesha

on the unit circle there are cos and sin (x,y)(cos,sin) x-coordinate represent cos y-coordinate represents sin so tan is sin over cos

30. anonymous

so then its -1?

31. anonymous

sin Θ = negative square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1?

32. Nnesha

yes right :=)

33. anonymous

thank you, would give 2 medals.. but one at a time :]

34. Nnesha

ahha that fine one medal is enough :) & my pleasure