x = 4 cos t, y = 4 sin t, π ≤ t ≤ 2 π?
Parametric equations for the motion of a particle in the xy -plane are given. Find a Cartesian equation for it. Indicate the portion of the graph traced by the particle.
- AshLv 710 months ago
x = 4 cos t
cos t = x/4 ...(1)
y = 4 sin t
sin t = y/4 ...(2)
We know sin²t + cos²t = 1
plug from (1) and (2)
y²/16 + x²/16 = 1
y² + x² = 16
y² = 16 - x² ....(3)
Since π ≤ t ≤ 2 π, we have -1≤cos t ≤1
so the condition for x is -1≤ x/4 ≤1 or -4≤x≤4
Also since π ≤ t ≤ 2 π, we have -1≤sin t ≤0
so the condition for y is -1≤ y/4 ≤0 or -4≤y≤0
Cartesian equation is y² = 16 - x²
-4≤x≤4 ; -4≤y≤0
The portion traced by the graph is in III and IV quadrant
- 10 months ago
Ask your math teacher.
Do you seriously think the brain dead idiots on Yahoo Answers who can't even write a complete sentence in English could possibly help you with your higher level mathematics equations?
- PopeLv 710 months ago
The parametric equations define a semicircle, centered on the origin, with radius 4, on or below the x-axis. Here is the Cartesian equation:
x² + y² = 16, y ≤ 0
y = -√(16 - x²)