91Ó°ÊÓ

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$x^{2}+y^{2}=9$$

Solve triangle. \(C=72^{\circ} 40^{\prime}, a=327 \mathrm{ft}, b=251 \mathrm{ft}\)

Velocity of a Star The space velocity \(\mathbf{v}\) of a star relative to the sun can be expressed as the resultant vector of two perpendicular vectors - the radial velocity \(\mathbf{v}_{r}\) and the tangential velocity \(\mathbf{v}_{t},\) where \(\mathbf{v}=\mathbf{v}_{r}+\mathbf{v}_{t} .\) If a star is located near the sun and its space velocity is large, then its motion across the sky will also be large. Barnard's Star is a relatively close star with a distance of 35 trillion mi from the sun. It moves across the sky through an angle of \(10.34^{\prime \prime}\) per year, which is the largest motion of any known star. Its radial velocity is \(\mathbf{v}_{r}=67 \mathrm{mi}\) per sec toward the sun. C. Jaschek, Astronomical Methods and Calculations, John Wiley and Sons.) (a) Approximate the tangential velocity \(\mathbf{v}_{t}\) of Barnard's Star. (Hint: Use the arc length formula \(s=r \theta\) from Section \(6.1 .\) ) (b) Compute the magnitude of \(\mathbf{v}\).

Find and graph all specified roots of \(i\) fourth

Determine the number of triangles ABC possible with the given parts. $$b=60, a=82, B=100^{\circ}$$

For each pair of vectors u and v with angle \(\theta\) between them, sketch the resultant. $$|\mathbf{u}|=20,|\mathbf{v}|=30, \theta=30^{\circ}$$

Write each complex number in rectangular form. 3 cis \(150^{\circ}\)

Write each complex number in rectangular form. 2 cis \(30^{\circ}\)

Solve triangle. \(A=112.8^{\circ}, b=6.28 \mathrm{m}, c=12.2 \mathrm{m}\)

In rectangular coordinates, the graph of $$a x+b y=c$$ is a horizontal line if \(a=0\) or a vertical line if \(b=0\). Work Exercises in order, to determine the general forms of polar equations for horizontal and vertical lines. Begin with the equation \(y=k,\) whose graph is a horizontal line. Make a trigonometric substitution for \(y\) using \(r\) and \(\theta\).