91Ó°ÊÓ

Find the exact polar coordinates of the points of intersection of graphs of the polar equations. Remember to check for intersection at the pole (origin). \(r^{2}=2 \sin (2 \theta)\) and \(r=1\)

Convert the point from polar coordinates into rectangular coordinates. \((10, \arctan (3))\)

In Exercises \(26-31,\) approximate the component form of the vector \(\vec{v}\) using the information given about its magnitude and direction. Round your approximations to two decimal places. \|\vec{v}\|=5280 ; \text { when drawn in standard position } \vec{v} \text { makes a } 12^{\circ} \text { angle with the positive } x \text { -axis }

The captain of the SS Bigfoot sees a signal flare at a bearing of \(\mathrm{N} 15^{\circ} \mathrm{E}\) from her current location. From his position, the captain of the HMS Sasquatch finds the signal flare to be at a bearing of \(\mathrm{N} 75^{\circ} \mathrm{W}\). If the SS Bigfoot is 5 miles from the HMS Sasquatch and the bearing from the SS Bigfoot to the HMS Sasquatch is \(\mathrm{N} 50^{\circ} \mathrm{E},\) find the distances from the flare to each vessel, rounded to the nearest tenth of a mile.

Find a parametric description for the given oriented curve. the curve \(y=4-x^{2}\) from (-2,0) to (2,0) (Shift the parameter so \(t=0\) corresponds to \((-2,0) .)\)

In Exercises \(21-40\), find the rectangular form of the given complex number. Use whatever identities are necessary to find the exact values. $$ z=3 \operatorname{cis}\left(\frac{4 \pi}{3}\right) $$

Convert the point from polar coordinates into rectangular coordinates. \(\left(-3, \arctan \left(\frac{4}{3}\right)\right)\)

Find a parametric description for the given oriented curve. the curve \(x=y^{2}-9\) from (-5,-2) to (0,3) .

Find the exact polar coordinates of the points of intersection of graphs of the polar equations. Remember to check for intersection at the pole (origin). \(r=4 \cos (2 \theta)\) and \(r=2\)

In Exercises \(26-31,\) approximate the component form of the vector \(\vec{v}\) using the information given about its magnitude and direction. Round your approximations to two decimal places. \|\vec{v}\|=450 ; \text { when drawn in standard position } \vec{v} \text { makes a } 210.75^{\circ} \text { angle with the positive } x \text { -axis }