Trigonometry

Trigonometry
Trigonometry is a branch of mathematics and by using some mathematical techniques, we can find the distances or heights. The word “Trigonometry” is derived from the Greek words “tri” (means three), ‘gon’
(means sides) and ‘metron’ (measure). Actually, Trigonometry is the study of relationships between the sides and angles of a triangle. Trigonometry is one of the most ancient subjects studied by scholars all over the world. The astronomers used trigonometry to calculate distance from the Earth to the planets and stars.

Trigonometry is also used in geography to construct maps, determine the position of an island in relation to the longitudes and latitudes, etc.

Trigonometric Ratios :
There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot. These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle ?.

Angle: A figure generated by rotating a given ray along of its end point.

Measurement of an Angle: Amount of rotation of the ray from initial position to the terminal position.

Hypotenuse Definition: the longest side of a right-angled triangle, opposite the right angle.

Perpendicular: at an angle of 90° to a given line, plane, or surface or to the ground.

Base: Side on which right angle triangle stands is known as its base

Opposite of Sin: Cosecant

Opposite of Cos: Secant

Opposite of Tan: Cotangent

Opposite of Cosecant: Sin

Opposite of Cotangent: Tan

Opposite of Secant: Cosecant

Trig Mnemonics: Some People Have, Curly Black Hair Through Proper Brushing.

Here, Some People Have is for

Sin ?= Perpendicular/ Hypotenuse.
Curly Black Hair is for

Cos ?= Base/ Hypotenuse.
Through Proper Brushing is for

Tan ?= Perpendicular/Base

The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains the same.
All six trigonometric ratios of an acute angle can be represented by? (theta), ß (Bita), Y (Gama),? (pie), ? (Sie), ? (Lamda),? (delta) etc.

Ratios of Complementary Angles
We know complementary angles are pair of angles whose sum is 90° Like 40°and 50°; 60°and 30°; 20°and 70°; 15° and 75° ; etc.

sin (90° – ?) = cos ?
cot (90° – ?) = tan?
cos (90° – ?) = sin ?
sec (90° – ?) = cosec ?
tan (90° – ?) = cot ?
cosec (90° – ?) = sec ?

Trigonometric Ratios of Some Specific Angles:
Values of Trigonometric ratios of 0o to 90o : (Table) :


Some Basic Trigonometric Identities:
csc? = 1sin? when sin0.
sec? = 1cos? when cos0.
cot? = 1tan? when tan? is defined and not 0.
sin? = 1csc? when csc? is defined and not 0.
cos? = 1sec? when sec? is defined and not 0.
tan? = 1cot? when cot? is defined and not 0.