Pre-Calculus Help?

What conic section is drawn by the parametric equations x=csc t and y cot?

A. Parabola

B. Circle

C. Ellipse

D. Hyperbola

  1. 👍
  2. 👎
  3. 👁
  1. Hey, you try some now !

    1. 👍
    2. 👎
  2. If your expression mean:

    x = csc t and y = cot t

    then:

    x = csc t

    x = 1 / sin t

    sin t = 1 / x

    y = cot t = cos t / sin t = ± √ ( 1 - sin² t ) / sin t = ± √ ( 1 - sin² t ) ∙ 1 / sin t =

    ± √ ( 1 - sin² t ) ∙ csc t = ± √ [ 1 - ( 1 / x )² ] ∙ x = ± √ ( x² / x² - 1 / x² ) ∙ x =

    ± √ [ ( x² - 1 ) / x² ] ∙ x =± [ √ ( x² - 1 ) / √ x² ] ∙ x =

    ± [ √ ( x² - 1 ) / x ] ∙ x = ± √ ( x² - 1 )

    y = ± √ ( x² - 1 )
    hyperbola

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the values of the six trigonometric functions of θ. (If an answer is undefined, enter UNDEFINED.) Function Value: csc(θ) = 4 Constraint: cot(θ) < 0 1) sin(θ)= 2) cos(θ)= 3) tan(θ)= 4) csc(θ)= 5) sec(θ)= 6) cot(θ)=

  2. maths

    Find parametric equations of the line that is tangent to the parabola y = x^2 at the point (−2, 4).

  3. Calc 3

    Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)

  4. pre cal

    What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola? (5 points) A) 3x^2 + y^2 + 12x - 7 = 0 B) 3x^2 + 3y^2 + 12x - 7 = 0 C) 3x^2 + y + 12x - 7 =

  1. math

    use the quotient and reciprocal identities to simplify the given expression cot t sin t csc t sin t tan t cot t cot t sec t

  2. Math

    Symmetric equations of a line are (x-1)/2 = (y+2)/-3 = (z-4)/5. Determine vector and parametric equations for the line. Is this right? v = < 2, -3, 5 > Parametric Equations: x = 1 + 2t y = -2 - 3t z = 4 + 5t

  3. Precalculus

    Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the

  4. Math

    Please Check My Answers!!! What is the type of conic section is given by the equation x^2-9y^2=900 and what is the domain and range? Answer: Type is hyperbola, Domain is all real values of x, not sure what the range is. Please

  1. Math

    Vector and parametric equations? A plane contains the point B(-3, 2, -4) and the line with parametric equations x = 1 + 2t, y = -t, z = -2 + 3t. Determine vector and parametric equations of the plane.

  2. Algebra 2

    How can you determine whether or not a graph, equation, or table of points is a conic section? Explain how to identify a conic section in each of these cases by giving examples.

  3. Math:)

    1. Simplify the expression. [csc^2(x-1)]/[1+sin x] a. csc x+1 b. csc x(csc x-1) c. sin^2 x-csc x**** d. csc^2 x-cos xtan x 2. Which of the following expressions can be used to complete the equation below? sec x/1+cot^2 x a. tan x

  4. Algebra II

    Am i correct? A plane intersects only one nappe of a double-napped cone. It is neither perpendicular to the cone's axis nor parallel to its generating line. Which conic section is formed? point circle ellipse

You can view more similar questions or ask a new question.