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    Formulae Sheet

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    rorosoto1
    This document contains a summary of trigonometric identities and formulas. It lists identities for addition, periodicity, cofunctions, double angles, half angles, Pythagorean identities, parity, and the laws of sines and cosines. Definitions for the sides and angles in the laws of sines and cosines are also provided in Figure 1.

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    Formulae Sheet

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    rorosoto1
    18 views1 page
    This document contains a summary of trigonometric identities and formulas. It lists identities for addition, periodicity, cofunctions, double angles, half angles, Pythagorean identities, parity, and the laws of sines and cosines. Definitions for the sides and angles in the laws of sines and cosines are also provided in Figure 1.

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    This document contains a summary of trigonometric identities and formulas. It lists identities for addition, periodicity, cofunctions, double angles, half angles, Pythagorean identities, parity, and the laws of sines and cosines. Definitions for the sides and angles in the laws of sines and cosines are also provided in Figure 1.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    18 views1 page

    Formulae Sheet

    Uploaded by

    rorosoto1
    This document contains a summary of trigonometric identities and formulas. It lists identities for addition, periodicity, cofunctions, double angles, half angles, Pythagorean identities, parity, and the laws of sines and cosines. Definitions for the sides and angles in the laws of sines and cosines are also provided in Figure 1.

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    © All Rights Reserved
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    Download as pdf or txt
    of 1

    Arkansas State University Campus Querétaro

    Formulae sheet - Trigonometric identities


    The use of this formulae sheet is subject to the authorization of your instructor.

    Other trigonometric functions: Addition identities:


    sin θ cos θ
    tan θ = cos θ cot θ = sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)
    sin θ
    1 1 cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)
    sec θ = cos θ csc θ = tan x ± tan y
    sin θ tan(x ± y) =
    Periodicity identities: 1 ∓ tan x tan y

    sin(x + 2π) = sin x cos(x + 2π) = cos x Double angle identities:


    sec(x + 2π) = sec x csc(x + 2π) = csc x
    sin(2x) = 2 sin x cos x
    tan(x + π) = tan x cot(x + π) = cot x
    cos(2x) = cos2 x − sin2 x
    Cofunction identities: = 1 − 2 sin2 x
    π 
    sin − x = cos x = 2 cos2 x − 1
     2π 
    cos − x = sin x Half angle identities:
     2π 
    tan − x = cot x 1h i
    2 sin2 x = 1 − cos(2x)
    2
    Pythagorean identities: 1h i
    cos2 x = 1 + cos(2x)
    sin2 x + cos2 x = 1 2
    1 + tan2 x = sec2 x Law of sines
    1 + cot2 x = csc2 x
    sin α sin β sin γ
    Parity identities: = =
    a b c
    Even Odd
    Law of cosines
    cos(−x) = cos(x) sin(−x) = − sin(x)
    sec(−x) = sec(x) csc(−x) = − csc(x) a2 = b2 + c2 − 2bc cos α
    tan(−x) = − tan(x) b2 = a2 + c2 − 2ac cos β
    cot(−x) = − cot(x) c2 = a2 + b2 − 2ab cos γ

    Figure 1: Definitions for the sides and angles appearing on the laws of sines and cosines

    Source: Dennis G. Zill, “Calculus. Early Transcendentals”, 4th edition, McGrawHill.

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