4. Without graphing, describe the curve produced by the equations x = cos 10t, y

Question

4. Without graphing, describe the curve produced by the equations x = cos 10t, y = sin 10t. 5. What is the effect of introducing a phase angle in the equations? For example, plot and describe the curves x = cos(5t + pi/4), y = sin 4t and x = cos(5t), y = sin 4t. What happens if you graph these parametric equations on a small interval like [0, pi]? 6. Graph the curve described by the equations x = cos2t, y = sin t. Eliminate the parameter by using the trigonometric identity, cos 2t = 1 - 2sin^2 t.

Explanation / Answer

Given that x = cos 10t and y = sin 10t

As cos^2 + sin ^2 = 1 for all angles

we have x^2+y^2 =1 and hence unit circle centred at origin.

6) x = cos2t and y = sint

i.e. x = 1-2sin^2 t = 1-2y^2

Or y^2 = (x+1)/2 hence a parabola with vertex at (-1,0)

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.