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Chapter 5: Problem 39
Use Heron's Area Formula to find the area of the triangle. $$a=1, \quad b=\frac{1}{2}, \quad c=\frac{3}{4}$$
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Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the given interval. $$2 \sec ^{2} x+\tan x-6=0, \quad\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$
Find the exact value of each expression. (a) \(\sin \left(\frac{7 \pi}{6}-\frac{\pi}{3}\right)\) (b) \(\sin \frac{7 \pi}{6}-\sin \frac{\pi}{3}\)
A batted baseball leaves the bat at an angle of \(\theta\) with the horizontal and an initial velocity of \(v_{0}=100\) feet per second. The ball is caught by an outfielder 300 feet from home plate (see figure). Find \(\theta\) if the range \(r\) of a projectile is given by \(r=\frac{1}{32} v_{0}^{2} \sin 2 \theta\).
Write the expression as the sine, cosine, or tangent of an angle. $$\cos 130^{\circ} \cos 40^{\circ}-\sin 130^{\circ} \sin 40^{\circ}$$
(a) use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval \([0,2 \pi),\) and (b) solve the trigonometric equation and demonstrate that its solutions are the \(x\) -coordinates of the maximum and minimum points of \(f .\) (Calculus is required to find the trigonometric equation.) Function $$f(x)=\sin x+\cos x$$ Trigonometric Equation $$\cos x-\sin x=0$$
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