108Chapter 5•Graphing and Inverse Functions§5.1It is worthwhile to remember the general shapes of the graphs of the six trigonometricfunctions, especially for sine, cosine, and tangent. In particular, the graphs of the sine andcosine functions are calledsinusoidalcurves. Many phenomena in nature exhibit sinusoidalbehavior, so recognizing the general shape is important.Example5.2Draw the graph ofy=1+cosxfor 0≤x≤2π.Solution:Adding a constant to a function just moves its graph up or down by that amount, depend-ing on whether the constant is positive or negative, respectively. So adding 1 to cosxmoves the graphofy=cosxupward by 1, giving us the graph ofy=1+cosx:xy012π4π23π4π5π43π27π42πy=1+cosxExercisesFor Exercises 1-12, draw the graph of the given function for 0≤x≤2π.1.y=−cosx2.y=1+sinx3.y=2−cosx4.y=2−sinx5.y=−tanx6.y=−cotx7.y=1+secx8.y=−1−cscx9.y=2sinx10.y=−3cosx11.y=−2tanx12.y
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