Sine, cosine and tangent they are divisions performed between the measurements of the sides of a right triangle. They can be used to relate these side measures to side measures. angles, forming a study known as Trigonometry. These divisions are known as reasonstrigonometric.
Definition of sine, cosine and tangent
If we consider a trianglerectangle any and we fix one of the other two angles α, we have:
sinα = leg opposite α
hypotenuse
cosα = leg adjacent to α
hypotenuse
tgα = leg opposite α
leg adjacent to α
catetoopposite, collaredadjacent and hypotenuse are the sides of the right triangle. To better understand these reasons, it is important to know these sides well as elements of the trianglerectangle.
Rectangle Triangle Elements
to be called trianglerectangle, that polygon, necessarily, need to have a anglestraight. The side of a right triangle that opposes the right angle is called hypotenuse. This side is also the largest of these triangles. The other two sides are called peccaries.
Fixing one of the other two
angles (α), we can determine which of the two peccaries é opposite and which one is adjacent at that angle. The side that is not one side of the angle is the opposite side. The other is the adjacent leg.The following image shows an example of a right triangle with its elements.
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the collared opposite at angle α is the side AB, the leg adjacent is the AC side and the hypotenuse is the BC side.
Sine, Cosine and Tangent Values
Sine, cosine and tangent have as results real numbers which vary according to the variation of the angle α. Two trianglesrectangles who also have a angle with the measure α will be obligatorily similar. Thus, the results of reasonstrigonometric evaluated in these two triangles will be equal, as their sides are proportional.
So, regardless of the lengths of the sides of a trianglerectangle that has an angle of 30°, for example, the sine of 30° will always be equal to 1/2, because in a right triangle that has an angle of 30°, the hypotenuse it is twice the length of the leg opposite this angle.
The following table shows the values for sinecosine and tangent From remarkable angles, that is, from the angles of 30°, 45° and 60°.
These values can be found through calculations in which we know the measurements of the internal angles of a triangle and from its sides. all angle in the range from 1st to 89th has values of sine, cosine and tangent. These values can be found in the complete table below:
By Luiz Paulo Moreira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "What are sine, cosine and tangent?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-sao-seno-cosseno-tangente.htm. Accessed on June 27, 2021.