Polar coordinates and parametric equations Quiz 1

Question 1

Write the value of $${{\left( {{x}^{2}}+{{y}^{2}} \right)}^{\frac{3}{2}}}$$ where $$x=\dfrac{9}{2}\,\sin \dfrac{\phi }{2}$$ and $$y=\dfrac{9}{2}\,\cos \dfrac{\phi }{2}$$

Accepted Answer

$$\dfrac{729}{8}$$

Answer

$$\dfrac{269}{4}$$

Answer

$$\dfrac{1024}{39}$$

Answer

$$\,\dfrac{864}{37}$$

Question 2

If $$x=\dfrac{r}{5}\cos m$$ and $$y=\dfrac{r}{5}\sin m$$ then what is the value of $$\dfrac{{{x}^{2}}}{{{y}^{2}}}$$ at $$m=\dfrac{\pi }{4}$$.

Accepted Answer

$$1$$

Answer

$$0$$

Answer

$$2$$

Answer

$$3$$

Question 3

If $$x+5\,\cos 	heta \,\,=5\,,\,\,\,y+5\sin 	heta =5$$, then evaluate $$\underset{	heta 	o 0}{\mathop{\lim }}\,\,\,\dfrac{x}{y}$$.

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$2$$

Answer

$$3$$

Question 4

For $$x=\dfrac{19}{5}\cos \left( \dfrac{t}{5} \right)$$ and $$y=\dfrac{19}{5}\,\sin \left( \dfrac{-t}{5} \right)$$, evaluate $$\int{\left( {{x}^{2}}+{{y}^{2}} \right)dt}$$.

Accepted Answer

$$\,\dfrac{361}{25}\,\,t+c$$

Answer

$$\dfrac{259}{25}\,\,t+c$$

Answer

$$\dfrac{621}{25}\,\,t+c$$

Answer

$$\dfrac{462}{25}\,\,t+c$$

Question 5

Write the value of $$\dfrac{d}{dq}\left( {{x}^{4}}+{{y}^{4}} \right)$$ if $${{\left( \dfrac{x}{3} \right)}^{2}}=\cos \left( \dfrac{q}{3} \right)$$ and $${{\left( \dfrac{y}{3} \right)}^{2}}=\sin \left( \dfrac{q}{3} \right)$$.

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$2$$

Answer

$$3$$