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Chapter 6: Problem 57
Under what conditions would you use Heron's formula to find the area of a triangle?
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Graph \(r_{1}\) and \(r_{2}\) in the same polar coordinate system. What is the relationship between the two graphs? $$r_{1}=4 \cos 2 \theta, r_{2}=4 \cos 2\left(\theta-\frac{\pi}{4}\right)$$
Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=2 \mathbf{i}+\mathbf{j}$$
What are parallel vectors?
Use a right triangle to write \(\sin \left(\cos ^{-1} x\right)\) as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. There are no points on my graph of \(r^{2}=9 \cos 2 \theta\) for which \(\frac{\pi}{4}<\theta<\frac{3 \pi}{4}\)
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