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). \(r=1-2 \cos (\theta)\) and \(r=1\)

In Exercises \(25-39,\) find a parametric description for the given oriented curve. the directed line segment from (3,-5) to (-2,2)

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}\|=392 \text { ; when drawn in standard position } \vec{v} \text { makes a } 117^{\circ} \text { angle with the positive } x \text { -axis }

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}\|=63.92 \text { ; when drawn in standard position } \vec{v} \text { makes a } 78.3^{\circ} \text { angle with the positive } x \text { -axis }

A hiker determines the bearing to a lodge from her current position is \(\mathrm{S} 40^{\circ} \mathrm{W}\). She proceeds to hike 2 miles at a bearing of \(\mathrm{S} 20^{\circ} \mathrm{E}\) at which point she determines the bearing to the lodge is \(\mathrm{S} 75^{\circ} \mathrm{W}\). How far is she from the lodge at this point? Round your answer to the nearest hundredth of a mile.

The angle of depression from an observer in an apartment complex to a gargoyle on the building next door is \(55^{\circ}\). From a point five stories below the original observer, the angle of inclination to the gargoyle is \(20^{\circ}\). Find the distance from each observer to the gargoyle and the distance from the gargoyle to the apartment complex. Round your answers to the nearest foot. (Use the rule of thumb that one story of a building is 9 feet.)

Find a parametric description for the given oriented curve. the circle \((x-3)^{2}+(y+1)^{2}=117\), oriented counter-clockwise

Discuss with your classmates why the Law of Sines cannot be used to find the angles in the triangle when only the three sides are given. Also discuss what happens if only two sides and the angle between them are given. (Said another way, explain why the Law of Sines cannot be used in the SSS and SAS cases.)

Find a parametric description for the given oriented curve. the triangle with vertices \((0,0),(3,0),(0,4),\) oriented counter-clockwise (Shift the parameter so \(t=0\) corresponds to \((0,0) .)\)

Use set-builder notation to describe the polar region. Assume that the region contains its bounding curves. The region inside the circle \(r=5\).