91Ó°ÊÓ

Find the angle between each pair of vectors. $$\mathbf{i}+7 \mathbf{j}, \mathbf{i}+\mathbf{j}$$

Find each quotient and express it in rectangular form by first converting the numerator and the denominator to trigonometric form. $$\frac{8}{\sqrt{3}+i}$$

The graph of \(r=a \theta\) is an example of the spiral of Archimedes. With a calculator set to radian mode. use the given value of a and interval of \(\theta\) to graph the spiral in the window specified. $$a=-1,0 \leq \theta \leq 12 \pi,[-40,40] \text { by }[-40,40]$$

Find each quotient and express it in rectangular form by first converting the numerator and the denominator to trigonometric form. $$\frac{2 i}{-1-i \sqrt{3}}$$

Find the angle between each pair of vectors. $$3 \mathfrak{i}+4 \mathfrak{j}, \mathfrak{j}$$

Find each quotient and express it in rectangular form by first converting the numerator and the denominator to trigonometric form. $$\frac{-i}{1+i}$$

Find the angle between each pair of vectors. $$\mathbf{i}+\mathbf{j}, 3 \mathbf{i}+4 \mathbf{j}$$

Find the polar coordinates of the points of intersection of the given curves for the specified interval of \(\theta\). $$r=4 \sin \theta, r=1+2 \sin \theta ; 0 \leq \theta<2 \pi$$

Find the polar coordinates of the points of intersection of the given curves for the specified interval of \(\theta\). $$r=3, r=2+2 \cos \theta ; 0^{\circ} \leq \theta<360^{\circ}$$

Find the area of each triangle. \(A=42.5^{\circ}, b=13.6\) meters, \(c=10.1\) meters