Table of Trigonometric Functions

Trigonometry came from the Greek words ‘trigon-triangle’ and ‘metron-measure’. Trigonometric functions generally define the function of angles. Relating the angles of triangle to its length of sides is the common use of trigonometric function. Table of trigonometric functions are generally applied in modeling periodic phenomena and study of triangles. Sin, cos, and tan are the most memorable trigonometric functions. Table of trigonometric functions refers to tabulating the trigonometric functions and trigonometric identities in order.

Having problem with Trigonometric Fourier Series keep reading my upcoming posts, i will try to help you.

Formulas in the Table of Trigonometric Functions:

• Sum-Difference Formula:

            Sin(A + B) = SinACosB + CosASinB                                   Sin(A − B) = SinACosB − CosASinB

            Cos(A + B) = CosACosB − SinASinB                                  Cos(A − B) = CosACosB + SinASinB

            Tan(A + B) = `(TanA + TanB)/ (1 - TanATanB)`                                        Tan(A − B) = `(TanA - TanB)/ (1 + TanATanB)`

• Sum-to-Product Formula:

            SinA + SinB = 2Sin(`(A + B) / 2` ) Cos(`(A - B) / 2` )                SinA − SinB = 2Cos(`(A + B) / 2` ) Sin(`(A - B) / 2` )

            CosA − CosB = 2Cos(`(A + B) / 2` ) Cos(`(A - B) / 2` )            CosA − CosB = −2Sin(`(A + B) / 2` ) Sin(`(A - B) / 2` )

• Product-to-Sum Formula:

            SinASinB = `1/2` [Cos(A − B) − Cos(A + B)]                           CosACosB = `1/2` [Cos(A − B) + Cos(A + B)]

            SinACosB = `1/2` [Sin(A + B) + Sin(A − B)]                            CosASinB = `1/2` [Sin(A + B) − Sin(A − B)]

Identities in the Table of Trigonometric Functions:

• Reciprocal identity,

              sin x = `1 / csc x` ,                  csc x = `1 / sin x` ,

              cos x = `1 / sec x` ,                 sec x = `1 / cos x` ,

              tan x = `1 / cot x` ,                   cot x = `1 / tan x` .

• Quotient identity,

              tan x = `sinx / cosx` ,

              cot x = `cosx / sinx` .

• Pythagorean identity,

              sin²x + cos²x = 1,

              1 + tan²x = sec²x,

              1 + cot²x = csc²x.

• Co-function identity,

              sin (90° − x) = cos x,            cos (90° – x) = sin x,               tan (90° − x) = cot x,

              csc (90° – x) = sec x,            sec (90° − x) = csc x,              cot (90° − x) = tan x.

• Even-Odd identity,

              sin (−x) = −sin x,                  cos (−x) = cos x,                     tan (−x) = −tan x,

              csc (−x) = −csc x,                 sec (−x) = sec x,                     cot (−x) = −cot x.

My forthcoming post is on Limit Laws and neet exam 2013 syllabus will give you more understanding about Algebra.

Example Using Table of Trigonometric Functions:

Ex: Prove that, sin⁴x + 2sin²x cos²x + cos⁴x = tan x cot x

Proof:     L.H.S. = sin⁴x + 2sin²x cos²x + cos⁴x

                               => (sin²x)² + 2sin²x cos²x + (cos²x)²

                               => (sin²x + cos²x)²

                               => (1)²

                               => 1

                   R.H.S. = tan x cot x

                               => `(sinx / cosx) xx (cosx / sinx )`

                               => 1

              => L.H.S. = R.H.S.

          Hence Proved that, sin⁴x + 2sin²x cos²x + cos⁴x = tanx cotx.