Processing Math: Done

From Förberedande kurs i matematik 1

Because the angle v satisfies v32, v belongs to the third quadrant in the unit circle. Furthermore, tanv=3 gives that the line which corresponds to the angle 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

a2+(3a)2=12

which gives us that 10a2=1 i.e. a=110. 

Thus, the angle v's x-coordinate is −110  and y-coordinate is −310 , i.e.

cosvsinv=−110=−310.