## GOODMAN 3 years ago Suppose (theta sign) is an angle in standard position whose terminal side lies in the given quadrant. For these functions, find the exact values of the remaining five trigonometric funtctions of (theta) sin(theta)=-4/5; Quadrant 4 tan(theta)=2; Quadrant 1

1. imranmeah91

sin(theta)=-4/5 |dw:1335488862320:dw|

2. imranmeah91

|dw:1335488894071:dw|

3. GOODMAN

How did you get that triangle?

4. imranmeah91

I drew a triangle and use the fact the sin (theta)=-4/5 remember sine is opposite over hypothenuse

5. GOODMAN

Ohhh, thats how you did it, okay!

6. GOODMAN

Now the 5 trig funtions of theta? I thought there were 3 trig functions o.O

7. imranmeah91

now let's find adjacent side value using pythagorean theorem a^2+4^2=5^2 a^2=25-16 a^2=9 a=3

8. imranmeah91

|dw:1335489127010:dw|

9. imranmeah91

now we can see what cos , and tan are cos is adjacent over hypotenuse cos(theta)= 3/5

10. imranmeah91

Tangent is sin(theta)/cos(theta) -4/5 ------ =-4/3 3/5

11. GOODMAN

Okay, i got those two, what are the other 3 they are looking for?

12. imranmeah91

csc(theta)= 1/sin(theta)= 1 = -5/4 ----- -4/5

13. imranmeah91

sec(theta)= 1/cos(theta)= 1/ (3/5) = 5/3

14. imranmeah91

cot(theta)= 1/tan(theta)= 1/(-4/3) =-3/4

15. GOODMAN

Oh we use the recriprocoals

16. imranmeah91

yep

17. GOODMAN

Ooooo, that makes much more sense!!! Okay, i know how to do the fraction one as we did now, but what about the second one, tan(theta)=2..how do i set that up?

18. imranmeah91

19. imranmeah91

use pythagorean theorem to find hypotenuse

20. GOODMAN

Okay, so basically, if its a whole number, we put it as a fraction?

21. imranmeah91

yes

22. GOODMAN

Hypotenuse is square root of 3

23. imranmeah91

sqrt[2^2+1^2]=sqrt[5]

24. GOODMAN

Srry, did it in my head, got my trusy calculator :D

25. GOODMAN

Okay, i got it, thanks for helpin :D

26. imranmeah91

anything for my shrink

27. GOODMAN

LOL, i might just pass algebra 2

28. imranmeah91

I took algebra 2 in sophomore year, and it was big deal way back

29. GOODMAN

Im taking it freshman :p

30. imranmeah91

smartie

31. GOODMAN

I wish, lol, i just barely pass every time.

32. imranmeah91

pre calc next year and then calculus

33. GOODMAN

arghhh..dont remind me :/ Im taking summer school to prep for it.