Solution 4.3:6a

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 3/4.

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 3/4.

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

b2+432=12

which gives that

b=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=34−74=−37.