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Chapter 5: Problem 61
Determine whether the statement is true or false. Justify your answer. In Heron's Area Formula, \(s\) is the average of the lengths of the three sides of the triangle.
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Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\cos \left(\theta+\frac{\pi}{2}\right)-\cos \left(\theta-\frac{\pi}{2}\right)$$
Determine whether the statement is true or false. Justify your answer. Complementary Angles If \(\phi\) and \(\theta\) are complementary angles, then show that (a) \(\sin (\phi-\theta)=\cos 2 \theta\) and \((\mathrm{b}) \cos (\phi-\theta)=\sin 2 \theta\).
Write the expression as the sine, cosine, or tangent of an angle. $$\sin 60^{\circ} \cos 15^{\circ}+\cos 60^{\circ} \sin 15^{\circ}$$
Find the exact value of the expression. $$\sin \frac{\pi}{12} \cos \frac{\pi}{4}+\cos \frac{\pi}{12} \sin \frac{\pi}{4}$$
Find the exact value of the trigonometric expression given that \(\sin u=-\frac{7}{25}\) and \(\cos v=-\frac{4}{5} .\) (Both \(u\) and \(v\) are in Quadrant III.) $$\cos (u+v)$$
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