Lösung 4.3:6c
Aus Online Mathematik Brückenkurs 1
Because the angle \displaystyle v satisfies \displaystyle \pi \le v\le 3\pi/2\,, \displaystyle v belongs to the third quadrant in the unit circle. Furthermore, \displaystyle \tan v = 3 gives that the line which corresponds to the angle \displaystyle v has slope 3.
In the third quadrant, we can introduce a right-angled triangle in which the hypotenuse is 1 and the sides have a 3:1 ratio.
If we now use the Pythagorean theorem on the triangle, we see that the horizontal side a satisfies
which gives us that \displaystyle 10a^{2}=1 i.e. \displaystyle a = 1/\!\sqrt{10}\,\textrm{.}
Thus, the angle v's x-coordinate is \displaystyle -1/\!\sqrt{10} and y-coordinate is \displaystyle -3/\!\sqrt{10}, i.e.
