Post a New Question

PRECALCULUS

posted by .

1.) determine two pairs of polar coordinates for the point (-4sqrt3, 4sqrt3)with 0degrees less than or equal to theta less than or equal to 360degrees


2.) Use DeMoivre's Theorem to find (1-i)^10. write your answer in the form a+bi.


3.) Find the cube roots of -8. Write your answer in form a+bi

  • PRECALCULUS -

    start with 3)

    3) -8=8@180

    roots: 2@60 and at each additional 120: 60, 180, 300

    lets do another just in case you need practice: fifth root of 32@55 deg

    on, 1/5 of 55 is 11. 1/5 of 360 is 72 so angles will be 11, then each 72 degrees for four additional roots. Notice the symettry when you sketch.

    now, the magnitude fifth root of 55 is 2.228


    2) 1-i= sqrt2@-45= sqrt2 @315

    take that to the tenth power: (sqrt2)^10 = 2^5=32

    angle? 315x10=3150
    lets do the negative angle -45. that times 10 is -450 or -90 = 270 Nice.

    then the answer is -32i

    check that.
    1) in polar, magnitude is sqrt(16*3*2)=9.80
    angle is 135

    check my work,I did most of this in my head with a migraine.

  • PRECALCULUS -

    1. x^2 + y^2 = r^2 = 16*3+16*3
    = 16*6
    so r = +/- 4 sqrt 6
    theta = 3 pi/4 or -pi/4

  • PRECALCULUS -

    2. r = sqrt(1+1) = sqrt 2
    theta = tan^-1 (1) = -pi/4
    so
    r e^i theta = sqrt 2 e^(-ipi/4 )

    sqrt 2^10 = 2^5 = 32

    -10 pi/4 = -5/2 pi = -pi /2 or -90

    32 (cos -90 + i sin -90)

    -32 i

  • PRECALCULUS -

    thank you guys so much! I had a really hard time with these. I appreciate it :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. alg

    the viewing window is defined by -3 is less than or equal to x is less than or equal to 7 and 10 is less than or equal to y is less than or equal to 30. give the approximate coordinates of a) the x-intercepts, b) the y-intercepts and …
  2. Trigonometry

    4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0 less …
  3. Math

    The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point for 0 is less than or equal to Q is less than 2pi. (-3,-3) My answers were (-3sqrt2, pi/4) and (pi/4, -3sqrt2). My teacher said that …
  4. Math

    The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point for 0 is less than or equal to Q is less than 2pi. (-3,-3) My answers were (-3sqrt2, pi/4) and (pi/4, -3sqrt2). My teacher said that …
  5. algebra/trigonometry

    What are the values of theta in the interval 0degrees less than or equal to theta less than or equal to 360 degrees that satisfy the equation tan theta - radical3=0
  6. Trig

    Solve: cos2x(2cosx+1) for 0degrees is less than or equal to x is equal to or less than 360degrees
  7. Precalculus

    A lattice point is a point with integer coordinates. How many lattice points (x,y) with -100 less than or equal to x less than or equal to 100 and -100 less than or equal to y less than or equal to 100 are on the graph of the parametric …
  8. Precalculus

    A lattice point is a point with integer coordinates. How many lattice points (x,y) with -100 less than or equal to x less than or equal to 100 and -100 less than or equal to y less than or equal to 100 are on the graph of the parametric …
  9. Precalculus

    Find two values for theta such that theta is greater than or equal to 0 but less than or equal to 2pi. 1. Tan theta=1.1071 2. Sin theta = -0.8818
  10. Precalculus

    Find two values for theta such that theta is greater than or equal to 0 but less than or equal to 2pi. 1. Tan theta=1.1071 2. Sin theta = -0.8818

More Similar Questions

Post a New Question