91Ó°ÊÓ

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.)

Convert the point from rectangular coordinates into polar coordinates with \(r \geq 0\) and \(0 \leq \theta<2 \pi\). $$ (-3,-\sqrt{3}) $$

Use parametric equations and a graphing utility to graph the inverse of \(f(x)=x^{3}+3 x-4\).

In Exercises \(41-50\), use set-builder notation to describe the polar region. Assume that the region contains its bounding curves. The region inside the cardioid \(r=2-2 \sin (\theta)\) which lies in Quadrants I and IV.

In Exercises \(41-50\), use set-builder notation to describe the polar region. Assume that the region contains its bounding curves. The region in Quadrant I which lies inside both the circle \(r=3\) as well as the rose \(r=6 \sin (2 \theta)\).

$$ r=\theta, 0 \leq \theta \leq 12 \pi $$

Use \(z=-\frac{3 \sqrt{3}}{2}+\frac{3}{2} i\) and \(w=3 \sqrt{2}-3 i \sqrt{2}\) to compute the quantity. Express your answers in polar form using the principal argument. $$ \left(\frac{w}{z}\right)^{6} $$

For the given vector \(\vec{v}\), find the magnitude \(\|\vec{v}\|\) and an angle \(\theta\) with \(0 \leq \theta<360^{\circ}\) so that \(\vec{v}=\|\vec{v}\|\langle\cos (\theta), \sin (\theta)\rangle\) (See Definition 11.8.) Round approximations to two decimal places. $$ \vec{v}=\langle-114.1,42.3\rangle $$

Find the indicated complex roots. Express your answers in polar form and then convert them into rectangular form. the two square roots of \(z=-25 i\)

Find the indicated complex roots. Express your answers in polar form and then convert them into rectangular form. the three cube roots of \(z=64\)