Trigonometry can be used in finding the measure of the angles, their function values and also the sides of a triangle. The 6 trigonometric functions can be used to find the remaining side or angle in a right triangle. These calculations give rise to trigonometric ratios in a right triangle.
In Trigonometry functions, angles and sides are widely used as they give rise to the Trigonometry functions. Based on the angles, there are 6 basic Trigonometric functions, out of which 3 are primary functions and the remaining three can be derived from the primary functions.
proportionality => Proportion is the equality shared between two ratios and when two separate ratios are equal to each other, they are said to be ‘in proportion’. Proportion is also the balance maintained between two sets of numbers divided with each other or two ratios.
Ratio is the comparison between two quantities which are similar and to compare they are divided by each other.
2 Dimensional Shapes – Geometry is the study of shapes and size. The structures are called 2-Dimensional shapes if they consist of only two dimensions and can be represented in x-y coordinate axis! The general dimensions for any 2-D geometric structure are the length and the width in the x and y direction.
Vectors: Any quantity can be described in 2 ways: a Scalar or Vector. ‘Scalar’ is a quantity which only has magnitude (number only). ‘Vector’ is a quantity which has both magnitude and direction (which way it’s heading towards).
What is a Function?
A function can be expressed in many ways, some of them being linear, quadratic, logarithmic functions etc. But just like numbers there are operations which can be used even on functions.
Addition and Subtraction between functions:
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Expression is a simple math relationship between a variable and a number. The variable is the quantity which can take any value accordingly (usually represented by an alphabet). However an Equation relates two different expressions with an ‘equality’ sign
Examples of Expressions:
Convergence and Divergence – In Sequences and Series, we can find whether the given function converges or diverges. A function is said to converge if its limit value exists and is finite. A function is said to diverge if it’s limit value does not exist(or rather approaches infinity).
Congruence geometry: If two objects are of same exact shape and same exact size, then they are called congruent objects. The congruent objects are more like duplicates of each other and fit perfectly when placed on top of each other.
In geometry, congruency is an important property and whenever two geometric shapes have same shape and length, then the angles of one shape are also equal to the other.
The symbol used to denote congruency is, ‘≡’ which means that the structures are of same shape and equal size.
Congruency in triangles:
SSS: 3 sides of one triangle=3 sides of the other
2) SAS :2 sides and included angle of one triangle=2 sides and included angle of other.
3)ASA :2 angles and included side one triangle= 2 angles and included side of other.
4) AAS :2angles and non-included side=2angles and non-included side of other
Example: If ∆ ABC≡∆DEF and BC=10 units, then EF=? EF=10 (since BC=EF )
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|You can also Read our other blog Angle Definition And Properties (Trigonometry)|