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Chapter 6: Problem 43
Find the inclination \(\theta\) (in radians and degrees) of the line. $$4 x+5 y-9=0$$
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Think About It \(\quad\) Explain what each of the following equations represents, and how equations (a) and (b) are equivalent. A. \(y=a(x-h)^{2}+k, \quad a \neq 0\) B. \((x-h)^{2}=4 p(y-k), \quad p \neq 0\) C. \((y-k)^{2}=4 p(x-h), \quad p \neq 0\)
(a) Show that the distance between the points \(\left(r_{1}, \theta_{1}\right)\) and \(\left(r_{2}, \theta_{2}\right)\) is \(\sqrt{r_{1}^{2}+r_{2}^{2}-2 r_{1} r_{2} \cos \left(\theta_{1}-\theta_{2}\right)}\) (b) Simplify the Distance Formula for \(\theta_{1}=\theta_{2} .\) Is the simplification what you expected? Explain. (c) Simplify the Distance Formula for \(\theta_{1}-\theta_{2}=90^{\circ}\) Is the simplification what you expected? Explain.
The graph of the parametric equations \(x=t\) and \(y=t^{2}\) is shown below. Determine whether the graph would change for each set of parametric equations. If so, how would it change? (GRAPH CANNOT COPY) (a) \(x=-t, y=t^{2}\) (b) \(x=t+1, y=t^{2}\) (c) \(x=t, y=t^{2}+1\)
In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$\theta=\pi / 6$$
In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$3 x+5 y-2=0$$
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