## anonymous one year ago Studying for a test and forgot how to do this In the triangle below, what ratio is sec θ? HYP = 3.9 ADJ =3.6 OPP = 1.5 My choices are 1. 12/13 2. 5/13 3. 13/12 4. 12/5

1. anonymous

@Nnesha @Hero @dan815

2. anonymous

picture?

3. Nnesha

draw a right triangle

4. anonymous

Well secant is 1/cosine. And I don't know if you ever learned this but my teachers always referred me back to SOHCAHTOA, Sine= opposite/hypotenuse Cosine = adjacent/hypotenuse Tangent = opposite/adjacent So from that you see that cosine is A/H and so secant would be H/A because it's the reciprocal So you have to see which answer is the same ratio as 3.9/3.6

5. Nnesha

|dw:1441061520659:dw|

6. Nnesha

what is the definition of sec ? reciprocal of sec = what ?

7. anonymous

Secant is the reciprocal of cosine so whatever cosine would be, say 3/4, secant would just be the reciprocal so 4/3

8. anonymous

cosine is the reciprocal right? @Nnesha

9. Nnesha

yes not cosine if sin = 1/csc then csc =1/sin

10. Nnesha

same with the sec

11. anonymous

Okay I'm still a little confused.

12. anonymous

What do I do to find the answer?

13. Nnesha

first of all you need to know $\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }$

14. Nnesha

sec is reciprocal of 1/cos now look at the diagram cos theta =?

15. anonymous

The secant would be the Hypotenuse/Adjacent So you would divide 3.9/3.6 which equals about 1.083 Then divide out the other answers to see which combination matches 1.083

16. anonymous

@hiltbrandj09 Okay I get it. So it would be 13/12 right?

17. anonymous

@Nnesha Do you think that is right?

18. anonymous

Thank you both so much!

19. anonymous

@marilynmonroe exactly!! & no problem (: