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Chapter 5: Problem 7
Determine the amplitude and period of each function. Then graph one period of the function. $$y=\sin 2 x$$
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Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \cos \left(\sin ^{-1} 2 x\right) $$
Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \cos \left(\sin ^{-1} \frac{1}{x}\right) $$
Explain how to find the length of a circular arc.
Exercises \(127-129\) will help you prepare for the material covered in the next section. In each exercise, let \(\theta\) be an acute angle in a right triangle, as shown in the figure. These exercises require the use of the Pythagorean Theorem. If \(a=1\) and \(b=1,\) find the ratio of the length of the side opposite \(\theta\) to the length of the hypotenuse. Simplify the ratio by rationalizing the denominator.
Your neighborhood movie theater has a 25 -foot-high screen located 8 feet above your eye level. If you sit too close to the screen, your viewing angle is too small, resulting in a distorted picture. By contrast, if you sit too far back, the image is quite small, diminishing the movie's visual impact. If you sit \(x\) feet back from the screen, your viewing angle, \(\theta,\) is given by $$\theta=\tan ^{-1} \frac{33}{x}-\tan ^{-1} \frac{8}{x}$$ (GRAPH CANNOT COPY) Find the viewing angle, in radians, at distances of 5 feet, 10 feet, 15 feet, 20 feet, and 25 feet.
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