Trigonometry (Law Of Cosines)

[DRACO]

In case of right angled triangles, C^2 = A^2 +B^2 - 2AB cos(Ψ) is shortened to C^2 = A^2 +B^2 because the cosine of the angle "Ψ" which is 90° is equal to 0. But how is its cosine equal to 0.

 

[OceanBreeze]

Try using the unit circle and it will make sense.

 

[sluggo]

Draco;

 

The Pythagorean theorem states

C^2 = A^2 +B^2.

Where did the other term come from?

[OceanBreeze]

 

Draco;

 

The Pythagorean theorem states

C^2 = A^2 +B^2.

Where did the other term come from?

 

 

The additional term comes from the Law of Cosines.

 

Pythagoras Theorem:

(only for Right-Angled Triangles)

a² + b² = c²

Law of Cosines:

(for all triangles)

a² + b² − 2ab cos© = c²

 

 

The Pythagorean theorem is a particular case of that law.

[sluggo]

The additional term comes from the Law of Cosines.

 

Pythagoras Theorem:

(only for Right-Angled Triangles)

a² + b² = c²

Law of Cosines:

(for all triangles)

a² + b² − 2ab cos© = c²

 

 

The Pythagorean theorem is a particular case of that law.

Thanks.