Anonymous
Anonymous asked in Science & MathematicsMathematics · 10 months ago

# 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.

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• MyRank
Lv 6
10 months ago

x = 4 cos t, y = 4 sin t,

x = 4cost

x² = 4²cos²t

x² = 16cos²t…(1

y = 4sint

y² = 4²sin²t

y² = 16 sin²t…(2)

from equation (1) and (2)

x² + y² = 16cos²t + 16 sin²t

x² + y² = 16(cos²t + sin²t)

x² + y² = 16

• Ash
Lv 7
10 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)

(y/4)²+(x/4)²=1

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

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?

• Pope
Lv 7
10 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

or

y = -√(16 - x²)