## Law of Sine Sinussatsen

One useful trigonometric formula can be obtained by expressing the area of an arbitrary triangle with sinus.

If one then proceeds to divide through by abc/2 one gets the Sinustheorem.

sinA/a = sinB/b= sinC/c

which is a relation between the sinus of the angle A and the side a standing opposite to angle A. By permutating the angles and sides you get the other two relations.

Another important  formula is the cosinetheorem:

c2 = a2+b2 – 2ab cos(c) $\\a^{2}=b^{2}+c^{2}-2bc\cdot cos\, \alpha \\$.

I angle a=90 this reduces to the Pythagoren theorem.

A beautiful proof  of this formula can be found with the aid of vectoranalysis:

compute (a+b)(a+b) = a2 +b2 + 2 a*b.

The last term is a scalar product between two vectors

a×b×cos(180-c) = -a×b×cos(c).

This gives the cosinetheorem:

c2 = a2+b2 – 2ab cos(c) Q.E.D.

Find the value of x Övning 1410 i Sjunnesson: en storks näbb är 26 cm lång. Hur stora matbitar kan den äta om den maximalt kan kan öppna munnen 41 grader?

Cosinussatsen ger:

x^2 = 26^2 + 26^2 – 2 26^2 *cos41 &times;  ## Om mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics
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