Solution 4.3:5

From Förberedande kurs i matematik 1

An often-used technique to calculate cosv and tanv, given the sine value of an acute angle, is to draw the angle v in a right-angled triangle which has two sides arranged so that sinv=57.

Using the Pythagorean theorem, we can determine the length of the third side in the triangle.

x2+52=72which gives thatx=72−52=24=26

Then, using the definition of cosine and tangent,

cosvtanv=x7=726=x5=526.

Note: The right-angled triangle that we use is just a tool and has nothing to do with the triangle that is referred to in the question.