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Solution 4.2:4c

From Förberedande kurs i matematik 1

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Current revision (08:41, 9 October 2008) (edit) (undo)
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In exercise 4.2:3e, we studied the angle <math>3\pi/4</math> and found that
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{{Displayed math||<math>\cos\frac{3\pi }{4} = -\frac{1}{\sqrt{2}}\qquad\text{and}\qquad\sin\frac{3\pi}{4} = \frac{1}{\sqrt{2}}\,\textrm{.}</math>}}
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Because <math>\tan x</math> is defined as <math>\frac{\sin x}{\cos x}</math>, we get immediately that
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{{Displayed math||<math>\tan\frac{3\pi}{4} = \frac{\sin\dfrac{3\pi}{4}}{\cos \dfrac{3\pi}{4}} = \frac{\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}} = -1\,\textrm{.}</math>}}

Current revision

In exercise 4.2:3e, we studied the angle 34 and found that

cos43=12andsin43=12.

Because tanx is defined as sinxcosx, we get immediately that

tan43=sin43cos43=1212=1.