Solution 4.2:3a

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A useful technique for calculating the value of a trigonometric function for angles that don't lie between
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<center> [[Image:4_2_3a.gif]] </center>
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<math>0</math>
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and
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<math>{\pi }/{2}\;</math>
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is to use the unit circle. If we draw a line which starts at the origin and makes a certain angle relative to the positive part of the
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<math>x</math>
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-axis, we can see that the cosine of that angle is the
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<math>x</math>
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-coordinate of the point of intersection between the line and the unit circle. In the same way, the sine of the angle is the
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<math>y</math>
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-coordinate of the intersection point.
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[[Image:4_2_3_a1.gif|center]]
[[Image:4_2_3_a1.gif|center]]
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In this case, we see immediately that
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<math>\text{sin}\left( -\frac{\pi }{2} \right)\text{ }=\text{ }-\text{1}</math>.
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[[Image:4_2_3_a2.gif|center]]
[[Image:4_2_3_a2.gif|center]]

Revision as of 11:47, 28 September 2008

A useful technique for calculating the value of a trigonometric function for angles that don't lie between \displaystyle 0 and \displaystyle {\pi }/{2}\; is to use the unit circle. If we draw a line which starts at the origin and makes a certain angle relative to the positive part of the \displaystyle x -axis, we can see that the cosine of that angle is the \displaystyle x -coordinate of the point of intersection between the line and the unit circle. In the same way, the sine of the angle is the \displaystyle y -coordinate of the intersection point.


In this case, we see immediately that \displaystyle \text{sin}\left( -\frac{\pi }{2} \right)\text{ }=\text{ }-\text{1}.


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