A more precise meaning :Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles.
Before getting into detail let us first understand it's uses in a practical situation.
1. The calculus is based on trigonometry and algebra.
2. The fundamental trigonometric functions like sine and cosine are used to describe the sound and light waves.
3. Trigonometry is used in oceanography to calculate heights of waves and tides in oceans.
4. It used in creation of maps.
5. It is used in satellite systems.
Notation of angles
The following Greek letters are used generally in trigonometry to indicate in a general way the number of degrees in angles;
theta (θ), phi (ϕ), alpha (α), beta (β), gamma (γ), etc.
Labeling the sides of a right-angled triangle
Hypotenuse is the the longest side of a right-angled triangle, opposite the right angle.
Perpendicular is the side opposite to the angle ( here in the diagram it is the θ ). It is also referred the opposite.
Adjacent side is the side next to the angle in question, the one other than the hypotenuse.
Generally it is the base of the triangle.
Trigonometrical ratios (t-ratios)
In a right angled triangle ,the three sides which gives six ratios, which are known as trigonometrical-ratios.
1.The ratio of the perpendicular to the hypotenuse is called sine of angle θ and it is written as sin θ.
sin θ = perpendicular / hypotenuse
2.The ratio of the base to the hypotenuse is called the cosine of angle θ and it is written as cos θ.
cos θ = base / hypotenuse
3.The ratio of the perpendicular to the base is called the tangent of angle θ and is written as tan θ.
tan θ = perpendicular / base
Reciprocal ratios
The following three are the reciprocals of the above ratios:
4. cosec θ = Hyp / Perp
5. sec θ = Hyp / Perp
6. cot θ = base / Perp
The above ratios shows that;
sinθ.cosecθ = 1
cosθ.secθ = 1
cotθ.tanθ = 1
Labeling the sides of a right-angled triangle
Hypotenuse is the the longest side of a right-angled triangle, opposite the right angle.Perpendicular is the side opposite to the angle ( here in the diagram it is the θ ). It is also referred the opposite.
Adjacent side is the side next to the angle in question, the one other than the hypotenuse.
Generally it is the base of the triangle.
Trigonometrical ratios (t-ratios)
In a right angled triangle ,the three sides which gives six ratios, which are known as trigonometrical-ratios.
1.The ratio of the perpendicular to the hypotenuse is called sine of angle θ and it is written as sin θ.
sin θ = perpendicular / hypotenuse
2.The ratio of the base to the hypotenuse is called the cosine of angle θ and it is written as cos θ.
cos θ = base / hypotenuse
3.The ratio of the perpendicular to the base is called the tangent of angle θ and is written as tan θ.
tan θ = perpendicular / base
Reciprocal ratios
The following three are the reciprocals of the above ratios:
4. cosec θ = Hyp / Perp
5. sec θ = Hyp / Perp
6. cot θ = base / Perp
The above ratios shows that;
sinθ.cosecθ = 1
cosθ.secθ = 1
cotθ.tanθ = 1
No comments:
Post a Comment