## highschoolmom2010 2 years ago The sine, cosine, and tangent ratios each have a reciprocal ratio. The reciprocal ratios are cosecant (csc), secant (sec), and cotangent (cot). use triangle ABC to write the definitions sec A csc B cot B

1. katherine.ok

Are you given or have you learned that csc= reciprocal of which , and sec of which , and cot is reciprocal of which?

2. highschoolmom2010

|dw:1376262907756:dw| not covered in my book so i kinda know a little

3. katherine.ok

csc= sin inverse. cot= tan inverse, sec= cos inverse. (Sorry for the informal uses of words)

4. katherine.ok

So the normal numerator of sin would be denomenator of csc , and etc..

5. highschoolmom2010

so its like flipped

6. tkhunny

For the sake of clarity, let's not use "inverse" in this manner. This is a reciprocal. I can see why you used "inverse", but a few lessons down the road, you WILL regret it if you call it that. Pick an Angle!! Let's call it "B". It your drawing, it's one of the acute angles. After that, the definitions require memorization. You will be required to know which side is adjacent to the given acute angle and which side is opposite the given acute angle. $$\sin(B) = \dfrac{m(Opposite\;Side)}{m(Hypotenuse)} = \dfrac{1}{\csc(B)}$$ $$\cos(B) = \dfrac{m(Adjacent\;Side)}{m(Hypotenuse)} = \dfrac{1}{\sec(B)}$$ $$\tan(B) = \dfrac{m(Opposite\;Side)}{m(Adjacent\;Side)} = \dfrac{1}{\cot(B)}$$

7. agent0smith

SecA = 1/cosA Find cosA first, this will let you find sec A. CosA = adjacent/hypotenuse. |dw:1376263854146:dw|

8. highschoolmom2010

cos A= 9/15

9. tkhunny

Yes!!!

10. highschoolmom2010

so would the sec A= 15/9?

11. agent0smith

Correct! Now try cscB = 1/sinB Sin = opp/hyp. |dw:1376264245185:dw|

12. highschoolmom2010

sin (b)=9/15

13. highschoolmom2010

csc=15/9

14. agent0smith

Correct. Now try cotB. cotB = 1/tanB.

15. highschoolmom2010

|dw:1376265085663:dw| $\tan (B)=\frac{ 9 }{ 12 }$

16. highschoolmom2010

cot B= 12/9

17. highschoolmom2010

@agent0smith do i have to simplify ^^

18. agent0smith

Yes, I would.

19. highschoolmom2010

so the cot (b)= 4/3 csc (B)=5/3 sec (B)=5/3

20. agent0smith

Yep :)

21. highschoolmom2010

cool i get it now :D ty

22. agent0smith

Oh except wasn't one of those sec A? secA was 5/3

23. highschoolmom2010

@agent0smith i have A written down lol

24. highschoolmom2010

ty @agent0smith @tkhunny & @katherine.ok for the help :D

25. agent0smith

Good job :)