savac 2 years ago Find the values of the six trigonometric functions of θ with the given constraint.Function value csc θ = 12, Constraint cot θ < 0

1. PeterPan

Well, let's just draw! :D |dw:1360754655516:dw|

2. PeterPan

Cosecant is just hypotenuse over the opposite side, right?

3. PeterPan

|dw:1360754762915:dw|

4. savac

5. PeterPan

Don't mistake cosine for cosecant, they're very different :D

6. PeterPan

Looked through your notes? Agree with me yet? :D

7. savac

im so confused. it says in my book COS(theta)=Adj/hyp

8. hartnn

@PeterPan did u just assume theta here : |dw:1360754965665:dw| because since cot theta is negative, theta is in 3rd quadrant. and so, measure of angle theta is between 180 and 270 degrees.

9. PeterPan

I drew this triangle with no coordinates in mind... should I have considered them? I was going to reason out that since cotangent is going to be negative, so should tangent, as it's just the reciprocal of tangent. Since cosecant is positive, so should sine, and since tangent, which is just sine over cosine, is negative, so should cosine and secant. :>

10. PeterPan

And lol @hartnn Cotangent is positive in the 3rd quadrant...

11. savac

im stll confused sir or ma'am

12. hartnn

sorry to confuse you savac , we have , cot as negative, means tan is negative. thats in 2nd or 3rd quadrant, now cosec is positive, means sin is positive, so, angle theta is in 2nd quadrant only. did u get this, first ?

13. hartnn

and we need to consider this ...as now the triangle will look like : |dw:1360755574255:dw|

14. savac

no, i got for my answers sin=1/12, cos=$\sqrt{143}$ /12 tan=1/$\sqrt{143}$ csc= 12 sec=12/$\sqrt{143}$ cot=$\sqrt{143}$/1

15. hartnn

you gotthat using identities, right ?

16. savac

i believe so

17. hartnn

okk, just make the cos, sec, tan and cot answers as negative. because theta lies in 2nd quadrant as i explained, where all these are negative.

18. savac

ok

19. hartnn

like $$\csc ^2 \theta -1 = \cot^2 \theta \\ \cot^2 \theta = 144-1=143 \\ \cot \theta = \pm \sqrt{143}$$ now we select NEGATIVE root , because cot <0 do, same thing for cos, sec, tan

20. hartnn

*so, $$\cot \theta = -\sqrt {143}$$

21. savac

so you use the same equation for cos, sec, tan

22. hartnn

same ? no for tan use tan = 1/ cot (since, you have cot) for sin use, sin = 1/csc (since, you have csc) for cos, use cos = tan / sin (since, now u have both, tan and sin) for sec, use sec = 1/ cos (since, now u have cos)

23. savac

ok so my answers would be sin=1/12 cos=-$\sqrt{143}$/12 tan= 1/-$\sqrt{143}$ csc= 12 sec=12/-$\sqrt{143}$ cot=-$\sqrt{143}$

24. PeterPan

Really sorry about disappearing, my internet isn't friendly to me today :(

25. savac

its ok. i am just glad you helped me. Thank you very much

26. savac

could you help me with a nother problem im having trouble with?

27. PeterPan

No problem :)