Pre calculus

in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates.

Thanks :)

asked by Meredith
  1. recall:
    sinØ = y/r and cosØ = x/r

    so:
    r= 5/(sin theta +2cos theta)
    r = 5/(y/r + 2x/r)
    r = 5/((2x+ y)/r)
    r = 5r/(2x + y)
    1 = 5/(2x+y)
    2x + y = 5 <----- a straight line

    proof:
    http://www.wolframalpha.com/input/?i=polar+plot+r%3D+5%2F(sin+theta+%2B2cos+theta)

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure
  2. 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
  3. Pre-Calculus

    1.) Which of the following polar equations is equivalent to the parametric equations below? x=t^2 y=2t A.) r=4cot(theta)csc(theta) B.) r=4tan(theta)sec(theta) C.) r=tan(theta)sec(theta)/4 D.) r=16cot(theta)csc(theta) 2.) Which
  4. Polar to Rectangular Form

    The letters r and theta represent polar coordinates. Write each equation in rectangular coordinates (x, y) form. Let t = theta (1) r = sin(t) + 1 (2) r = sin(t) - cos(t)
  5. Trig

    Which expression equivalent to: cos(theta + pi/2). A)cos theta B)-cos theta C)sin theta D)-sin theta my book doesnt give examples of this but my crack at it would be C b/c distributive property? and 2cos theta = sin theta
  6. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2
  7. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2
  8. Pre-Calculus

    translate this polar equation into a rectangular form: rsin(2theta)=sin(theta) My answer: r2sin(theta)cos(theta)=sin(theta) 2rcos(theta)=1 2x=1 x=1/2 This is the only answer I can get and someone told me it's wrong. Would someone
  9. Advanced Math

    Identify the polar form of the linear equation 4x+3y=10. x=rcos(theta),y=rsin(theta) 4x+3y=4rcos(theta)+3rsin(theta)=10 r=10/(4cos(theta)+3sin(theta) I got it wrong
  10. Algebra II

    Multiple Choice Which expression is NOT equivalent to 1? (theta) means 0 with dash in it. A.)sin^2 (theta)+cot^2 (theta) sin^2 (theta) B.)(sin^(theta))/(1-cos(theta))-cos(theta) C,)sec^2 (theta)+ tan^2 (theta) D.)(cot^2(theta)

More Similar Questions