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Solution 4.3:2b

From Förberedande kurs i matematik 1

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Current revision (13:14, 9 October 2008) (edit) (undo)
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If we write the angle
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If we write the angle <math>\frac{7\pi }{5}</math> as
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<math>\frac{7\pi }{5}</math>
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as
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{{Displayed math||<math>\frac{7\pi}{5} = \frac{5\pi+2\pi}{5} = \pi + \frac{2\pi }{5}</math>}}
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<math>\frac{7\pi }{5}=\frac{5\pi +2\pi }{5}=\pi +\frac{2\pi }{5}</math>
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we see that <math>7\pi/5</math> is an angle in the third quadrant.
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[[Image:4_3_2_b.gif||center]]
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we see that
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The angle between <math>0</math> and <math>\pi</math> which has the same ''x''-coordinate as the angle <math>7\pi/5</math>, and hence the same cosine value, is the reflection of the angle <math>7\pi/5</math> in the ''x''-axis, i.e.
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<math>\frac{7\pi }{5}</math>
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is an angle in the third quadrant.
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<center> [[Image:4_3_2_b.gif]] </center>
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{{Displayed math||<math>v = \pi -\frac{2\pi}{5} = \frac{3\pi}{5}\,\textrm{.}</math>}}
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the line
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<math>x=\cos \frac{7\pi }{5}</math>
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The angle between
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<math>0</math>
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and
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<math>\pi </math>
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which has the same x-coordinate as the angle
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<math>{7\pi }/{5}\;</math>, and hence the same cosine value, is the reflection of the angle
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<math>{7\pi }/{5}\;</math>
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in the
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<math>x</math>
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-axis, i.e.
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<math>v=\pi -\frac{2\pi }{5}=\frac{3\pi }{5}</math>.
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Current revision

If we write the angle 57 as

57=55+2=+52

we see that 75 is an angle in the third quadrant.

The angle between 0 and which has the same x-coordinate as the angle 75, and hence the same cosine value, is the reflection of the angle 75 in the x-axis, i.e.

v=−52=53.
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