Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pi$$
A) $x ^ { 2 } + y ^ { 2 } = 49$; for $x$ in $- 7 \leq x \leq 7$
B) $y = x ^ { 2 } - 9$; for $x$ in $- 2 \leq x \leq 2$
C) $y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 49$; for $x$ in $- \infty

Question

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pi$$
A) $x ^ { 2 } + y ^ { 2 } = 49$; for $x$ in $- 7 \leq x \leq 7$
B) $y = x ^ { 2 } - 9$; for $x$ in $- 2 \leq x \leq 2$
C) $y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 49$; for $x$ in $- \infty < x < \infty$
D) $\mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 49$; for $\mathrm { x }$ in $- \infty < \mathrm { x } < \infty$

Quizplus · Accepted Answer

Using the trigonometric identity $\sin^2 t + \cos^2 t = 1$, we can eliminate the parameter $t$ by squaring both parametric equations and adding them: $x^2 + y^2 = 49\sin^2 t + 49\cos^2 t = 49(\sin^2 t + \cos^2 t) = 49$. This represents a circle with radius 7, hence the domain for $x$ is correctly given as $-7 \leq x \leq 7$.

Find a Rectangular Equation for the Plane Curve Defined by the Parametric