A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Mirandaregina

  • one year ago

If csc theta = √5, then what is cot theta?

  • This Question is Closed
  1. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is the reciprocal of csc ?

  2. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha Sine

  3. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not just sin :=) 1/sin = csc so csc = ?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    In addition to sine, cosine, and tangent, there are three other trigonometric functions you need to know for the Math IIC: cosecant, secant, and cotangent. These functions are simply the reciprocals of sine, cosine, and tangent. Cotangent is the reciprocal of tangent.

  5. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha so csc = 1/sine

  6. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes right so if csc = sqrt{5} then sin = ???

  7. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    remember thy are reciprocal of each other

  8. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha then sin = 1/√5 = √5/5 ?

  9. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    draw a triangle and label its opposite side 1 and its hypotenuse sqr(5)

  10. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm \[\csc = \frac{ \sqrt{5} }{ 1 } ~~~~~ \sin=\frac{ 1 }{ \sqrt{5} }\] so draw right triangle for now it's okay leave the radical sign at the denominator |dw:1440603990058:dw| \[\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }\]

  11. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha so if sin theta = opp/hyp, and opp is 1 and hyp is √5, is it √5/5?

  12. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes right sin = opp .hyp|dw:1440604248339:dw| apply the Pythagorean theorem to find 3rd side of right triangle

  13. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes you could use sqr(5) for the opposite side and 5 for the hypotenuse but 1 and sqr(5) seem easier (smaller numbers) but either set will give the same answer.

  14. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha 1^2 + √5^2 = 6

  15. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    c^2 = a^2 + b^2 the unknown is a leg.

  16. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    c=hypotenuse(longest leg of right triangle )

  17. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Nnesha @phi did I use the Pythagorean Theorem correctly? doesn't a = 1 and b = √5 ?

  18. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no a and b are the legs you know a and c (and you need to find b, the other leg)

  19. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you know the hypotenuse (because sin is opp/hyp) you know a side and the hypotenuse

  20. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1440604696536:dw|

  21. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi how do I find b?

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    quick question is 1/3 a rational number

  23. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a^2 + b^2 = c^2 put in numbers for a and c can you do that ?

  24. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi but does a = 1? because before I said 1^2 + √5^2 = 6

  25. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a=1 and c= \( \sqrt{5} \) put those in the formula \[a^2 + b^2 = c^2\]

  26. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    notice c is on the other side of the = sign from a and b

  27. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i guess she is trying to say that sqrt of 5 +1 equal to 6

  28. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    square of sqrt 5**

  29. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when you write 1^2 + √5^2 = c^2 a^2 + b^2 = c^2 that means a is 1 and b is sqr(5). but that is not what we want

  30. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi I understand, thanks :) so I'm not sure if I did this right but I have 1^2 + b^2 = √5 b + 1^2 = √5 b^2 + 1 - 1 = √5 - 1 b^2 = √1.236068

  31. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    almost, but the formula says c^2 so you want (sqrt(5))^2

  32. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi as is √1.111786 = 1.0544126

  33. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    *as in

  34. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you wrote 1^2 + b^2 = √5 but what it should be is 1^2 + b^2 = (√5)^2 now find b

  35. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi oh my mistake 1^2 + b^2 = (√5)^2 b = 2

  36. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. now you know all 3 sides of the triangle |dw:1440605865953:dw|

  37. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the want the cotangent of theta (I would write the tangent of theta, then "flip it" to make it the cotangent) or you can remember cotangent is adj/opp

  38. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi cot theta = adj/opp = 2/1 = 2

  39. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  40. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi so that's the overall answer? I got that answer when I first tried it but I thought it was wrong! lol

  41. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now you know how to do it so you believe it

  42. Mirandaregina
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @phi @Nnesha thank you for all your help and patience everyone :)

  43. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my pleasure o^_^o

  44. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.