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

1. PeterPan Group Title

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

2. PeterPan Group Title

Cosecant is just hypotenuse over the opposite side, right?

3. PeterPan Group Title

|dw:1360754762915:dw|

4. savac Group Title

5. PeterPan Group Title

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

6. PeterPan Group Title

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

7. savac Group Title

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

8. hartnn Group Title

@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 Group Title

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 Group Title

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

11. savac Group Title

im stll confused sir or ma'am

12. hartnn Group Title

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 Group Title

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

14. savac Group Title

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 Group Title

you gotthat using identities, right ?

16. savac Group Title

i believe so

17. hartnn Group Title

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 Group Title

ok

19. hartnn Group Title

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 Group Title

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

21. savac Group Title

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

22. hartnn Group Title

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 Group Title

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 Group Title

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

25. savac Group Title

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

26. savac Group Title

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

27. PeterPan Group Title

No problem :)