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Half Angle Formulas, Formulas of semiperimeter, Laws and Formulas, Properties of Trigonometric Functions

Trigonometry

Trigonometric functions are related with the properties of triangles. Some laws and formulas are also derived to tackle the problems related to triangles, not just right-angled triangles.

Half Angle Formulas

With the introduction of the semiperimeter concept, the half angle identities of trigonometric functions can also be expressed in term of the semi-perimeter of a triangle or sides of a triangle.

The half angle formula for the sine funcion of an internal angle of a triangle can be obtained from the half angle identities of sine function by substituting the result of cosine function formula. Imply

The half angle formula for the cosine funcion of an internal angle of a triangle can be obtained from the half angle identities of cosine function by substituting the result of cosine function formula. Imply

The half angle formula for the tangent funcion of an internal angle of a triangle can be obtained from the half angle identities of tangent function by substituting the result of cosine function formula or from the half angle formula for sine and cosine functions directly. Imply

Link:http://output.to/sideway/default.asp?qno=130600026

HTMLCommon Greek in Unicode

html ENTITIES Greek in Unicode

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Β	Β	Β	Β	Β	greek capital letter beta	U+0392
Γ	Γ	Γ	Γ	Γ	greek capital letter gamma	U+0393
Δ	Δ	Δ	Δ	Δ	greek capital letter delta	U+0394
Ε	Ε	Ε	Ε	Ε	greek capital letter epsilon	U+0395
Ζ	Ζ	Ζ	Ζ	Ζ	greek capital letter zeta	U+0396
Η	Η	Η	Η	Η	greek capital letter eta	U+0397
Θ	Θ	Θ	Θ	Θ	greek capital letter theta	U+0398
Ι	Ι	Ι	Ι	Ι	greek capital letter iota	U+0399
Κ	Κ	Κ	Κ	Κ	greek capital letter kappa	U+039A
Λ	Λ	Λ	Λ	Λ	greek capital letter lambda	U+039B
Μ	Μ	Μ	Μ	Μ	greek capital letter mu	U+039C
Ν	Ν	Ν	Ν	Ν	greek capital letter nu	U+039D
Ξ	Ξ	Ξ	Ξ	Ξ	greek capital letter xi	U+039E
Ο	Ο	Ο	Ο	Ο	greek capital letter omicron	U+039F
Π	Π	Π	Π	Π	greek capital letter pi	U+03A0
Ρ	Ρ	Ρ	Ρ	Ρ	greek capital letter rho	U+03A1
Σ	Σ	Σ	Σ	Σ	greek capital letter sigma	U+03A3
Τ	Τ	Τ	Τ	Τ	greek capital letter tau	U+03A4
Υ	Υ	Υ	Υ	Υ	greek capital letter upsilon	U+03A5
Φ	Φ	Φ	Φ	Φ	greek capital letter phi	U+03A6
Χ	Χ	Χ	Χ	Χ	greek capital letter chi	U+03A7
Ψ	Ψ	Ψ	Ψ	Ψ	greek capital letter psi	U+03A8
Ω	Ω	Ω	Ω	Ω	greek capital letter omega	U+03A9
α	α	α	α	α	greek small letter alpha	U+03B1
β	β	β	β	β	greek small letter beta	U+03B2
γ	γ	γ	γ	γ	greek small letter gamma	U+03B3
δ	δ	δ	δ	δ	greek small letter delta	U+03B4
ε	ε	ε	ε	ε	greek small letter epsilon	U+03B5
ζ	ζ	ζ	ζ	ζ	greek small letter zeta	U+03B6
η	η	η	η	η	greek small letter eta	U+03B7
θ	θ	θ	θ	θ	greek small letter theta	U+03B8
ι	ι	ι	ι	ι	greek small letter iota	U+03B9
κ	κ	κ	κ	κ	greek small letter kappa	U+03BA
λ	λ	λ	λ	λ	greek small letter lambda	U+03BB
μ	μ	μ	μ	μ	greek small letter mu	U+03BC
ν	ν	ν	ν	ν	greek small letter nu	U+03BD
ξ	ξ	ξ	ξ	ξ	greek small letter xi	U+03BE
ο	ο	ο	ο	ο	greek small letter omicron	U+03BF
π	π	π	π	π	greek small letter pi	U+03C0
ρ	ρ	ρ	ρ	ρ	greek small letter rho	U+03C1
&sigmaf;	ς	ς	ς	ς	greek small letter final sigma	U+03C2
σ	σ	σ	σ	σ	greek small letter sigma	U+03C3
τ	τ	τ	τ	τ	greek small letter tau	U+03C4
υ	υ	υ	υ	υ	greek small letter upsilon	U+03C5
φ	φ	φ	φ	φ	greek small letter phi	U+03C6
χ	χ	χ	χ	χ	greek small letter chi	U+03C7
ψ	ψ	ψ	ψ	ψ	greek small letter psi	U+03C8
ω	ω	ω	ω	ω	greek small letter omega	U+03C9
&thetasym;	ϑ	ϑ	ϑ	ϑ	greek theta symbol	U+03D1
&upsih;	ϒ	ϒ	ϒ	ϒ	greek upsilon with hook symbol	U+03D2
	ϕ	ϕ	ϕ	ϕ	greek phi symbol	U+03D5
ϖ	ϖ	ϖ	ϖ	ϖ	greek pi symbol	U+03D6

Link:http://output.to/sideway/default.asp?qno=130600024

Triagonometric Formulas, Formulas of semiperimeter, Laws and Formulas, Properties of Trigonometric Functions

Trigonometry

Trigonometric functions are related with the properties of triangles. Some laws and formulas are also derived to tackle the problems related to triangles, not just right-angled triangles.

Trigonometric Formulas

With the introduction of the semiperimeter concept, the trigonometric functions can also be expressed in term of the semi-perimeter of a triangle or sides of a triangle. From the cosine rules, the cosine function of an internal angle of a triangle which is expressed in term of the sides of a triangle can also be transformed in term of semiperimeter. Imply

The sine function of an internal angle of a triangle can also be obtained by equating the area of triangle formulas and the Heron's formula together. Imply

The sine and cosine functions of an internal angle of a triangle can also be expressed in terms of sides of triangle. Imply

The tangent function of an internal angle of a triangle can also be expressed in terms of sides of triangle using the sine and cosine function of the internal angle accordingly. Imply

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