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Calculus - Parametric Curve and Area

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Figure 3 shows the curve C with parametric equations ... (a) Find the value of t at the point P ...
[See the attached questions file.]

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x = 8 cos t and y = 4 sin 2t
P(x, y) = (4, 2√3)
∴ 4 = 8 cos t and 2√3 = 4 sin 2t
cos t = ½ and
sin 2t = 2√3 /4 = √3 /2
2 sin t cos t = √3 /2 ==> 2 sin t (1/2) = √3 /2 ==> sin t = √3 /2
This gives t = π/3

At t = π/3, ...

Solution Summary

Neat, step-by-step solutions to the parametric curve and area are provided for all parts of the question.

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