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Magazine Problem 60
Write the first expression in terms of the second if the terminal point determined by \(t\) is in the given quadrant. \(\csc t,\) cot \(t ; \quad\) Quadrant III
Problem 60
Graph \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$f(x)=\sin x, \quad g(x)=\sin 2 x$$
Problem 61
Write the first expression in terms of the second if the terminal point determined by \(t\) is in the given quadrant. \(\tan t, \sec t ; \quad\) Quadrant III
Problem 61
Graph the three functions on a common screen. How are the graphs related? $$y=x^{2}, \quad y=-x^{2}, \quad y=x^{2} \sin x$$
Problem 62
Write the first expression in terms of the second if the terminal point determined by \(t\) is in the given quadrant. \(\sin t,\) sec \(t ; \quad\) Quadrant IV
Problem 62
Graph the three functions on a common screen. How are the graphs related? $$y=x, \quad y=-x, \quad y=x \cos x$$
Problem 63
Graph the three functions on a common screen. How are the graphs related? $$y=\sqrt{x}, \quad y=-\sqrt{x}, \quad y=\sqrt{x} \sin 5 \pi x$$
Problem 63
Write the first expression in terms of the second if the terminal point determined by \(t\) is in the given quadrant. \(\tan ^{2} t, \sin t ; \quad\) any quadrant
Problem 64
Write the first expression in terms of the second if the terminal point determined by \(t\) is in the given quadrant. \(\sec ^{2} t \sin ^{2} t, \cos t ; \quad\) any quadrant
Problem 64
Graph the three functions on a common screen. How are the graphs related? $$y=\frac{1}{1+x^{2}}, \quad y=-\frac{1}{1+x^{2}}, \quad y=\frac{\cos 2 \pi x}{1+x^{2}}$$
