Processing Math: Done

From Förberedande kurs i matematik 1

If we think of the angle v as an angle in the unit circle, then v lies in the fourth quadrant and has x -coordinate 43.

If we enlarge the fourth quadrant, we see that we can make a right-angled triangle with hypotenuse equal to 1 and an opposite side equal to 43.

Using Pythagoras' theorem, it is possible to determine the remaining side from

b2+432=12 

which gives that

b2+432=12b=1−432=1−916=716=47 

Because the angle v belongs to the fourth quadrant, its y -coordinate is negative and is therefore equal to −b, i.e.

sinv=−47 

Thus, we have directly that

tanv=sinvcosv=43−47=−37