91Ó°ÊÓ

suppose \(z=r(\cos \theta+i \sin \theta)\) Use vectors to show that $$ -z=r[\cos (\theta+\pi)+i \sin (\theta+\pi)] $$

Given \(\mathbf{u}=\langle- 2,5\rangle\) and \(\mathbf{v}=\langle 4,3\rangle,\) find each of the following. $$2 \mathbf{u}+\mathbf{v}-6 \mathbf{v}$$

Find the area of triangle \(A B C\). \(a=154 \mathrm{cm}, b=179 \mathrm{cm}, c=183 \mathrm{cm}\)

Write each vector in the form a\mathbf{i} \(+b \mathbf{j}\) $$\langle- 5,8\rangle$$

A flagpole 95.0 ft tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is \(35.0^{\circ},\) and the angle of elevation of the bottom of the flagpole is \(26.0^{\circ} .\) Find the height of the building.

Use a graphing calculator window of \([-1250,1250]\) by \([-1250,1250],\) in degree mode, to graph more of \(r=2 \theta\) (a spiral of Archimedes) than what is shown in Figure \(71 .\) Use \(-1250^{\circ} \leq \theta \leq 1250^{\circ} .\)

Find the area of triangle \(A B C\). \(a=25.4\) yd, \(b=38.2\) yd, \(c=19.8\) yd

A pilot flies her plane on a heading of \(35^{\circ} 00^{\prime}\) from point \(X\) to point \(Y,\) which is 400 \(\mathrm{mi}\) from \(X .\) Then she turns and flies on a heading of \(145^{\circ} 00^{\prime}\) to point \(Z,\) which is \(400 \mathrm{mi}\) from her starting point \(X .\) What is the heading of \(Z\) from \(X\), and what is the distance \(Y Z ?\)

Write each vector in the form a\mathbf{i} \(+b \mathbf{j}\) $$\langle 6,-3\rangle$$

Write each vector in the form a\mathbf{i} \(+b \mathbf{j}\) $$\langle 2,0\rangle$$