Processing Math: Done

From Förberedande kurs i matematik 1

We draw an angle v in the unit circle, and the fact that sin v =310 means that its y -coordinate equals 310.

With the information that is given, we can define a right-angled triangle in the second quadrant which has a hypotenuse of 1 and a vertical side of length 310.

We can determine the triangle's remaining side by using Pythagoras' theorem,

a2+3102=12 

which gives that

a=1−3102=1−9100=91100=1091 

This means that the angle's x -coordinate is −a, i.e. we have

cosv=−1091 

and thus

tanv=sinvcosv=310−1091=−391