# tringle

Forums Leaving Cert Maths tringle

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• #12499 Anonymous

tringles????

• #12500 Anonymous

Trigonometric triangles?

• #12501 Anonymous
• #12502 Anonymous

i have a huge problem in understandind any thing too do with tringles.Could you help

• #220 Anonymous

:tringles????

• #12503

If you mean triangles they have three corners?

• #12504

Courtesy of http://www.wikipedia.org
A triangle is a shape. It has three straight sides and three points. The three angles of a triangle add to 180 degrees. It is the polygon with the least possible number of sides.

Types of triangles
A right triangle that is also isosceles
A right triangle that is also isosceles

Triangles can be grouped according to how long their sides are

* In an equilateral triangle all three sides have the same length
* In an isosceles triangle two sides have the same length
* In a scalene triangle all sides have different lengths

Triangles can also be grouped by their angles.

* A right triangle has one angle that is 90 degrees (a right angle). The side opposite the right angle is the hypotenuse.
* An obtuse triangle has one angle that is larger than 90 degrees (an obtuse angle)
* An acute triangle has angles that are all less than 90 degrees (acute angles)

Trigonometry
Trigonometry uses a large amount of specific words to describe parts of a triangle. Some of the definitions in trigonometry are:

* Right triangle – A right triangle is a triangle that has one angle that is equal to 90 degrees. (A triangle can not have more than one right angle.) The standard trigonometric ratios can only be used on right triangles.
* Hypotenuse – The hypotenuse of a triangle is the longest side, and the side that is opposite the right angle. For example, for the triangle on the right, the hypotenuse is side c.
* Opposite of an angle – The opposite side of an angle is the side that does not intersect with the vertex of the angle. For example, side a is the opposite of angle A in the triangle to the right.
* Adjacent of an angle – The adjacent side of an angle is the side that intersects the vertex of the angle but is not hypotenuse. For example, side b is adjacent to angle A in the triangle to the right.

Trigonometric Functions
There are 6 trigonometric functions:
Sine
Cosine
Tangent
Cotangent
Secant
Cosecant.

Trigonometric Ratios

There are three main trigonometric ratios, and three inverses of those ratios. There are 6 total ratios. They are:

Sine (sin) – The sine of an angle is equal to the {Opposite over Hypotenuse}

Cosine (cos) – The cosine of an angle is equal to the {Adjacent over Hypotenuse}

Tangent (tan) – The tangent of an angle is equal to the {Opposite over Adjacent}

The reciprocals (multiplicative inverse) of these ratios are:

Cosecant (cosec) – The cosecant of an angle is equal to the {Hypotenuse over Opposite} or cosec.theta = {1 over sin.theta}

Secant (sec) – The secant of an angle is equal to the {Hypotenuse over Adjacent} or sec.theta = {1 over cos.theta}

Cotangent (cot) – The cotangent of an angle is equal to the {Adjacent over Opposite} or cot .theta = {1 over tan.theta}

Some Important Identities
tan x = sin x over cos x
cotan x = cos x over sin x
sec x = 1over cos x
cosec x = 1 over sin x
sin2x + cos2x = 1
sin (x+x) = 2sin x.cos x
cos (x+x) = cos x cos x – sin x sin x = cos squared x – sin squared x
sin (x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y – cos x sin y
cos (x+y) = cos x cos y – sin x sin y
cos (x-y)= cos x cos y + sin x sin y

They mean tringles. The ones that don’t look like sqlares or cicles. 