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    Trigonometric Formulas Identities

    Uploaded by

    Christian Alonzo
    This document outlines various trigonometric formulas and identities including: 1) Reciprocal relations defining trig functions like sin, cos, tan, csc, sec, and cot. 2) Pythagorean identities relating trig functions of the same angle. 3) Definitions of trig functions like tan and cot. 4) Formulas for trig functions of sums and differences of angles. 5) Formulas for trig functions of twice an angle. 6) Formulas for trig functions of half an angle. 7) Formulas for sums and differences of trig functions.

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    © All Rights Reserved
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    Trigonometric Formulas Identities

    Uploaded by

    Christian Alonzo
    13 views2 pages
    This document outlines various trigonometric formulas and identities including: 1) Reciprocal relations defining trig functions like sin, cos, tan, csc, sec, and cot. 2) Pythagorean identities relating trig functions of the same angle. 3) Definitions of trig functions like tan and cot. 4) Formulas for trig functions of sums and differences of angles. 5) Formulas for trig functions of twice an angle. 6) Formulas for trig functions of half an angle. 7) Formulas for sums and differences of trig functions.

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    Trigo Formulas

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    This document outlines various trigonometric formulas and identities including: 1) Reciprocal relations defining trig functions like sin, cos, tan, csc, sec, and cot. 2) Pythagorean identities relating trig functions of the same angle. 3) Definitions of trig functions like tan and cot. 4) Formulas for trig functions of sums and differences of angles. 5) Formulas for trig functions of twice an angle. 6) Formulas for trig functions of half an angle. 7) Formulas for sums and differences of trig functions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    13 views2 pages

    Trigonometric Formulas Identities

    Uploaded by

    Christian Alonzo
    This document outlines various trigonometric formulas and identities including: 1) Reciprocal relations defining trig functions like sin, cos, tan, csc, sec, and cot. 2) Pythagorean identities relating trig functions of the same angle. 3) Definitions of trig functions like tan and cot. 4) Formulas for trig functions of sums and differences of angles. 5) Formulas for trig functions of twice an angle. 6) Formulas for trig functions of half an angle. 7) Formulas for sums and differences of trig functions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    of 2

    TRIGONOMETRIC FORMULAS AND IDENTITIES

    A. Reciprocal Relations
    & &
    sin 𝐴 = csc 𝐴 =
    '(' ) (+, )

    & &
    cos 𝐴 = (.' ) sec 𝐴 = '0( )

    & &
    tan 𝐴 = '03 ) cot 𝐴 = 34, )

    B. Pythagorean Relations

    sin5 𝐴 + cos 5 𝐴 = 1

    tan5 𝐴 + 1 = sec 5 𝐴

    cot 5 𝐴 + 1 = csc 5 𝐴

    C. By Definition

    (+, ) '0( )
    tan 𝐴 = '0( ) cot 𝐴 = (+, )

    D. Functions of Sum and Difference of Angles

    sin(𝐴 ± 𝐵) = sin 𝐴 cos 𝐵 ± cos 𝐴 sin 𝐵


    cos(𝐴 ± 𝐵) = cos 𝐴 cos 𝐵 ∓ sin 𝐴 sin 𝐵
    tan 𝐴 ± tan 𝐵
    tan(𝐴 ± 𝐵) =
    1 ∓ tan 𝐴 tan 𝐵
    cot 𝐴 cot 𝐵 ∓ 1
    cot(𝐴 ± 𝐵) =
    cot 𝐵 ± cot 𝐴

    E. Functions of Twice an Angle

    sin 2𝐴 = 2 sin 𝐴 cos 𝐴

    cos 2𝐴 = cos 5 𝐴 − sin5 𝐴

    = 2 cos 5 𝐴 − 1

    = 1 − 2 sin5 𝐴
    2 tan 𝐴
    tan 2𝐴 =
    1 − tan5 𝐴
    cot 5 𝐴 − 1
    cot 2𝐴 =
    2 cot 𝐴
    F. Functions of Half-Angle

    1 1 − cos 𝐴
    sin 𝐴 = ±?
    2 2

    1 1 + cos 𝐴
    cos 𝐴 = ±?
    2 2

    1 1 − cos 𝐴 sin 𝐴 1 − cos 𝐴


    tan 𝐴 = ±? = =
    2 1 + cos 𝐴 1 + cos 𝐴 sin 𝐴

    1 1 + cos 𝐴 1 + cos 𝐴 sin 𝐴


    cot 𝐴 = ±? = =
    2 1 − cos 𝐴 sin 𝐴 1 − cos 𝐴

    G. Sum and Difference of Functions


    1 1
    sin 𝐴 + sin 𝐵 = 2 sin (𝐴 + 𝐵) cos (𝐴 − 𝐵)
    2 2
    1 1
    sin 𝐴 − sin 𝐵 = 2 cos (𝐴 + 𝐵) sin (𝐴 − 𝐵)
    2 2
    1 1
    cos 𝐴 + cos 𝐵 = 2 cos (𝐴 + 𝐵) cos (𝐴 − 𝐵)
    2 2
    1 1
    cos 𝐴 − cos 𝐵 = −2 sin (𝐴 + 𝐵) sin (𝐴 − 𝐵)
    2 2
    2 sin 𝐴 cos 𝐵 = sin(𝐴 + 𝐵) + sin(𝐴 − 𝐵)
    2 cos 𝐴 sin 𝐵 = sin(𝐴 + 𝐵) − sin(𝐴 − 𝐵)
    2 cos 𝐴 cos 𝐵 = cos(𝐴 + 𝐵) + cos(𝐴 − 𝐵)
    2 sin 𝐴 sin 𝐵 = −cos(𝐴 + 𝐵) + cos(𝐴 − 𝐵)

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