Question
Obtain the graph of the cosine function for ? ? [0,2?].
Answer :
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The cosine function is given by [ y=\cos x,\qquad x\in[0,2\pi]. ] To obtain its graph, we first consider the important values of (x) between (0) and (2\pi). The standard values of the cosine function are: [ \begin{array}{c|ccccc} x&0&\frac{\pi}{2}&\pi&\frac{3\pi}{2}&2\pi\ \hline \cos x&1&0&-1&0&1 \end{array} ] Thus, the corresponding points are [ (0,1),\quad \left(\frac{\pi}{2},0\right),\quad (\pi,-1),\quad \left(\frac{3\pi}{2},0\right),\quad (2\pi,1). ] These points are plotted on the Cartesian plane, with (x) on the horizontal axis and (y) on the vertical axis. The maximum value of the cosine function is (1), while its minimum value is (-1). Therefore, the graph lies completely between the horizontal lines
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