Trigonometric

Trigonometric
* Trigonometric function of any angle
A “rectangular coordinate system” in a plane consists in two perpendicular number lines (called axis), one horizontal and the other vertical,which intersection point (origin) is the zero of each scale. It is used to select the positive direction, in the horizontal scale (X axis), to the right of the origin and upwards of the origin in thevertical scale (Y axis).
The axes divide the plane in four parts called “quadrants” and it is numerated in contrary sense of the clockwise counter. The numerated “quadrants”, which the sign of thecoordinates of a point in each one of them
In general, the value of the angle of reference of an angle depends on the quadrant in which R is located. If θ is a positive angle in normal position andthe terminal side of θ is in the:
Quadrant I | Then | Θr=θ |
Quadrant II | Then | Θr=180°- θ |
Quadrant III | Then | Θr= θ-180° |
Quadrant IV | Then | Θr=360°- θ |

The signs of thefunctions for each quadrant, we can summarize the results in the next table
| Sin θ | Cos θ | Tan θ | Cot θ | Sec θ | Csc θ |
I | + | + | + | + | + | + |
II | + | - | - | - | - | + |
III | - | - | +| + | - | - |
IV | - | + | - | - | + | - |

* Oblique angles-Cosine law
Cosine Law can be used directly when you know two sides and the included angle.
Cosine law is usually written as:a2=b2+c2-2bc Cos A
In the same way the Cosine Law can be written in the following form if the other data are given:
b2=a2+c2-2ac Cos B and c2=a2+b2-2ab Cos C.

x² = 10² + 14² −2(10)(14)cos(44°)
x² =296 −280cos(44)
x² = 94.6

* Area of a triangle
From geometry you can find that area of a triangle is: rea=bh2 , this formula can be convert in another formula that is Area=12ac Sin BArea=12ac Sin B=125(11) Sin 11
7
5
40=17.67

* Oblique triangles-Sine Law
This formula is called Sine Law and it is equal to the Sine of the...