Solution 4.4:1d
From Förberedande kurs i matematik 1
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- | {{ | + | Because <math>\tan v = \frac{\sin v}{\cos v}</math>, the condition <math>\tan v = 1</math> gives <math>\sin v = \cos v</math>, i.e. we look for angles in the unit circle whose ''x''- and ''y''-coordinates are equal. |
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- | + | After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, <math>v=\pi/4</math> and <math>v = \pi + \pi/4 = 5\pi/4\,</math>. | |
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+ | [[Image:4_4_1_d.gif|center]] |
Current revision
Because \displaystyle \tan v = \frac{\sin v}{\cos v}, the condition \displaystyle \tan v = 1 gives \displaystyle \sin v = \cos v, i.e. we look for angles in the unit circle whose x- and y-coordinates are equal.
After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, \displaystyle v=\pi/4 and \displaystyle v = \pi + \pi/4 = 5\pi/4\,.