91Ó°ÊÓ

Approximate the area of a parallelogram that has sides of lengths a and \(b\) (in feet) if one angle at a vertex has measure \(\boldsymbol{\theta}.\) \(a=40.3, \quad b=52.6, \quad \theta=100^{\circ}\)

Approximate the horizontal and vertical components of the vector that is described. Jet's approach A jet airplane approaches a runway at an angle of \(7.5^{\circ}\) with the horizontal, traveling at a speed of \(160 \mathrm{mi} / \mathrm{hr}\)

Express in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$8\left(\cos \frac{7 \pi}{4}+i \sin \frac{7 \pi}{4}\right)$$

Express in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$6\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)$$

Find a unit vector that has (a) the same direction as the vector a and (b) the opposite direction of the vector a. $$\mathbf{a}=-8 \mathbf{i}+15 \mathbf{j}$$

Express in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$12\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right)$$

Find a unit vector that has (a) the same direction as the vector a and (b) the opposite direction of the vector a. $$\mathbf{a}=5 \mathbf{i}-3 \mathbf{j}$$

Find a unit vector that has (a) the same direction as the vector a and (b) the opposite direction of the vector a. $$\mathbf{a}=\langle 2,-5\rangle$$

Express in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$5(\cos \pi+i \sin \pi)$$

Find a unit vector that has (a) the same direction as the vector a and (b) the opposite direction of the vector a. $$\mathbf{a}=\langle- 12,5\rangle$$