Let $\mathcal{G}$ be the graph of the parametric equations
x &= \cos(4t),\\
y &= \sin(6t).
\end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces the entire graph $\mathcal{G}$?

  1. 👍 0
  2. 👎 0
  3. 👁 1,008
  1. since cos(4t) has period pi/2
    and sin(6t) has period pi/3

    the LCM is pi

    1. 👍 0
    2. 👎 0
  2. That answer keeps on coming as wrong, I had gotten that answer earlier. I am not sure what is wrong :(

    1. 👍 0
    2. 👎 0
  3. its pi/2

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig

    Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) -

  2. geometry

    Find the measure of the acute angle x, if : sin(x)=0.0175; sin(x)=0.5015; cos(x)=0.06814; cos(x)=0.0670. I know that Sin(x)=opp./hyp. and that cos(x)=adj./hyp. but i have no clue about how to find the xs in these equations

  3. Pre-Cal (Trig) Help?

    The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty

  4. Math

    The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0

  1. math

    Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t) - cos(t) + C s(t) = -cos(t) - sin(t) + Cx + D


    Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π A. x2 - y2 = 6; -6 ≤ x ≤ 6 B. x2 - y2 = 36; -6 ≤ x ≤ 6 C. x2 + y2 =

  3. precalculus

    To what interval I must we restrict the parameter t if the graph of the parametric equations x=t+1 y = 2t^2 +1 for t in the set I is identical to the graph of the parametric equations x = 1+ sin s y = 2- cos(2s) for s in [0,pi)?

  4. MATH

    A lattice point is a point with integer coordinates. How many lattice points $(x,y)$ with $-100\le x\le 100$ and $-100\le y\le 100$ are on the graph of the parametric equations \begin{align*} x&=30-40\cos t,\\ y&=-50 + 30\cos t?

  1. Calculus

    Find the velocity, v(t), for an object moving along the x-axis in the acceleration, a(t), is a(t)=cos(t)-sin(t) and v(0)=3 a) v(t)=sin(t) + cos(t) +3 b) v(t)=sin(t) + cos(t) +2 c) v(t)= sin(t) - cos(t) +3 d) v(t)= sin(t) - cos(t)

  2. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with

  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. math;)

    Show that sin(x+pi)=-sinx. So far, I used the sum formula for sin which is sin(a+b)=sin a cos b+cos a sin b. sin(x+pi)=sin x cos pi+cos x sin pi I think I am supposed to do this next, but I am not sure. sin(x+pi)=sin x cos x+sin

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