Also called Nepero’s law, but it was described in the 13th century by Persian mathematician Nasir al-Din al-Tusi (1201–74), who also presented the law of sines for plane triangles in his five-volume work Treatise on the Quadrilateral. Proof: To prove the Law of tangents we follow these steps: Consider law ..
It’s also known as the cosine formula or cosine rule, and it relates the lengths of the sides of a triangle to the cosine of one of its angles. In a scalene triangle the square of a side is given by the sum of the squares of other sides, minus twice the product ..
In a scalene triangle a side is given by sum of products of eachone of other two sides times the cosin of adjacent angle from this side and the first side: Projection law or the formula of projection law express the algebraic sum of the projection of any two side in term of the third ..
According to notation conventions, we call sides and verticies of a scalene triangle as show the figure: Figure By Ant.ton.t – Own work, CC BY-SA 3.0, also we call internal angle of the triangle respectively the internal angle of verticies: A, B, C from Wikipedia: The law of sines, sine law, sine formula, or sine ..
Topography notes: Table of contents If we want to solve a right-triangle, we need at least two elements; one of wich must be a side of the triangle. In the conventional notation the name of sides, angles and vertex of a right triangle are as show in this figure: Case a) hypotenuse a and B-angle ..
Topography notes: Table of contents Consider this figure: Point B give a right triangle (ABC) into the circumference. , and . We know the definitions of trignometric functions (1), and we can consider complementar angle of (2). We have these relations by (1) and (2): Then: According to the definitions above it is possible ..
Topography notes: Table of contents Trigonometric equations have as variables trigonometric functions. They can be solved using the algebraic methods and trigonometric formulas. There are no specific rules to solve trigonometric equations, but often with some steps the equation is simplify to a one trigonometric variable. Another way to solve these is using graphs. Where the graph of the ..
In this post I give the geometrical demonstration of two trigonometric formulas from which are the source of all others. We consider an arch of a circle with radius r=1, we consider two points P and P’, the angles are respectively and . Now we demonstrate these formulas: (1) (2) Now we ..
We consider this figure: If we consider the triangle OPP” and the isosceles triangle OPP’ and we call , we can write this relation: is the chord of the arch . With the relation we can obtain some relations. For the chord of the arch from and – is . This is a side of a regular hexagon, ..
We consider again this figure: If we consider the triangle OPP” we can write this relation using Pitagora’s theorem: by this, leads to the following fundamental relations between trigonometric function of a same angle: With these relations it is possible obtain all trigonometric function by only one for a same angle. In fact only applying ..