Question

Define Trigonometry
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Answer 1

Step-by-step explanation:

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.

For a trigonometric function, the length of one complete cycle is called a period. ... In general, we have three basic trigonometric functions like sin, cos and tan functions, having -2π, 2π and π period respectively. Sine and cosine functions have the forms of a periodic wave: Period: It is represented as “T”.

The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. This makes Hipparchus the founder of trigonometry.

There are three basic trigonometric ratios: sine , cosine , and tangent

Answer 2

Answer:

Trigonometry is a branch of Mathematics, that involves the study of the relationship between angles and lengths of triangles. 

Basic Concepts

Here are the domain and range of basic trigonometric functions:

Sine function, sine: R → [– 1, 1]

Cosine function, cos : R → [– 1, 1]

Tangent function, tan : R – { x : x = (2n + 1) π/2, n ∈ Z} →R

Cotangent function, cot : R – { x : x = nπ, n ∈ Z} →R

Secant function, sec : R – { x : x = (2n + 1) π/2, n ∈ Z} →R – (– 1, 1)

Cosecant function, cosec : R – { x : x = nπ, n ∈ Z} →R – (– 1, 1)

Properties of Inverse Trigonometric Functions

sin-1 (1/a) = cosec-1(a), a ≥ 1 or a ≤ – 1

cos-1(1/a) = sec-1(a), a ≥ 1 or a ≤ – 1

tan-1(1/a) = cot-1(a), a>0

sin-1(–a) = – sin-1(a), a ∈ [– 1, 1]

tan-1(–a) = – tan-1(a), a ∈ R

cosec-1(–a) = –cosec-1(a), | a | ≥ 1

cos-1(–a) = π – cos-1(a), a ∈ [– 1, 1]

sec-1(–a) = π – sec-1(a), | a | ≥ 1

cot-1(–a) = π – cot-1(a), a ∈ R

Addition Properties of Inverse Trigonometry functions

sin-1a + cos-1a = π/2, a ∈ [– 1, 1]

tan-1a + cot-1a = π/2, a ∈ R

cosec-1a + sec-1a = π/2, | a | ≥ 1

tan-1a + tan-1 b = tan-1 [(a+b)/1-ab], ab<1

tan-1a – tan-1 b = tan-1 [(a-b)/1+ab], ab>-1

tan-1a – tan-1 b = π + tan-1[(a+b)/1-ab], ab > 1; a,b > 0

Twice of Inverse of Tan Function

2tan-1a = sin-1 [2a/(1+a2)], |a| ≤ 1

2tan-1a = cos-1[(1-a2)/(1+a2)], a ≥ 0

2tan-1a = tan-1[2a/(1+a2)], – 1 < a < 1

Step-by-step explanation:

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