law of cosines and sines?

Question

what are they, and has anyone ever made a program for a ti-83+ calculator that calculates them.

Answer 1

Law of sines:

(sin a/ A) = (sin b/ B) = (sin c/ C)

- Only works for a triangle
- a, b, and c represent different the three angles of the triangle
- A, B, and C represent the different lengths of the triangle.
- The sin of an angle, a, divided by its opposite, A, side is equal to the sin of another angle, b, divided by that other angles side, B, and that is equal to the sin of the last angle, c, divided by that side of the triangle, C.

Law of cosines:

C² = A² + B² − 2AB cos θ

- Only works for trinagles
- A, B, and C represent the different lengths of the triangle.
- θ, or thada, is an angle that falls between the sides A and B.
- This is the real version of the pythagorean theorem because if θ was equal to 90 degress then you would be left with C² = A² + B², because cos 90 = 0 and eliminates the last term of − 2AB cos θ!

Answer 2

Consider a triangle ABC, with sides a, b and c and angles A, (opposite do side A) B and C,

The law of cosines says that a^2 = b^2 + c^2 - 2bc cos A. Of course, similar equations hold for the other angles

The law of sines say a/sin A = b/sin B = c/sin C = D, where D is the diameter of the circle circunscribed to the trinagle.

I can compute such angles and sides using an Excel spreadsheet.

Answer 3

Law of Sines:

For a triangle with angles A, B and C and sides a, b and c,

(sin A)/a = (sin B)/b = (sin C)/c


Law of Cosines:

For a triangle with angles A, B and C and sides a, b and c,

c^2 = a^2 + b^2 - (2ab cos C)

(note that the Pythagorean Theorem is a special case of the Law of Cosines. When angle C is 90 degrees, the final term drops out, leaving c^2 = a^2 + b^2)

Answer 4

Nomenclature: perspective C is the perspective in the time of from section c on the triangle ABC. Sine regulation works for all triangles; a/sin A = b/sin B = c/sin C. till you admit the possibility of actual 0-perspective triangles; the regulation is invalid for that case. Cosine regulation works for all triangles, besides. a^2 + b^2 - 2 a*b*cos C = c^2 some regulations could require particular situations, yet none of them basically state that the triangle won't be able to have a ideal perspective. so far as i comprehend, those 2 regulations haven't any particular exceptions.

Answer 5

Law of cosines:

c² = a² + b² - 2ab*cos(C)

Law of sines:

sin(A)/a = sin(B)/b = sin(C)/c

These formulas can be used to find unknown angles and sides of triangles. Here is a link to a program for both the TI-83+ and TI-84+ that solves triangles using the two formulas:

http://www.ticalc.org/archives/files/fileinfo/224/22471.html