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    θ= cosθ sinθ csc θ=1+cot θ θ secθcosθ sinθ: csc = Product to Sum

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    Israel Sapnu Jr.
    1) The csc function can be expressed as the ratio of 1 to the sin function or as the product of sec and cos over sin. 2) The tan function can be expressed as the ratio of sin to cos or as cot to 1 over cos. 3) The Pythagorean identity states that 1 over sin squared is equal to 1 over sin squared plus cot squared.

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    θ= cosθ sinθ csc θ=1+cot θ θ secθcosθ sinθ: csc = Product to Sum

    Uploaded by

    Israel Sapnu Jr.
    28 views2 pages
    1) The csc function can be expressed as the ratio of 1 to the sin function or as the product of sec and cos over sin. 2) The tan function can be expressed as the ratio of sin to cos or as cot to 1 over cos. 3) The Pythagorean identity states that 1 over sin squared is equal to 1 over sin squared plus cot squared.

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    Original Title

    Trigonometry-Identities

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    1) The csc function can be expressed as the ratio of 1 to the sin function or as the product of sec and cos over sin. 2) The tan function can be expressed as the ratio of sin to cos or as cot to 1 over cos. 3) The Pythagorean identity states that 1 over sin squared is equal to 1 over sin squared plus cot squared.

    Copyright:

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

    θ= cosθ sinθ csc θ=1+cot θ θ secθcosθ sinθ: csc = Product to Sum

    Uploaded by

    Israel Sapnu Jr.
    1) The csc function can be expressed as the ratio of 1 to the sin function or as the product of sec and cos over sin. 2) The tan function can be expressed as the ratio of sin to cos or as cot to 1 over cos. 3) The Pythagorean identity states that 1 over sin squared is equal to 1 over sin squared plus cot squared.

    Copyright:

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

    cosθ

    Reciprocal Identity cotθ=


    sinθ

    1 1
    ( )( ) = csc 2 θ=1+ cot2 θ
    sin θ sin θ

    secθcosθ
    1. cscθ = Product to Sum
    sinθ

    1
    Recall: 4. -sinAsinB= [cosA cosB-sin AsinB-
    2
    (cosAcos+sinAsinB)

    1 1
    secθ=¿ = [cosA cosB-sin AsinB-(cosAcos-
    cosθ 2
    sinAsinB)

    1
    cscθ = cos θ )
    ( cos θ 1
    -sinAsinB = [-2sinAsinB]
    2
    sinθ
    1
    cscθ= -sinAsinB =-sinAsinB
    sin θ
    cscθ=csc θ
    sec θ cos θ
    ∴cscθ= Half Angle
    sin θ
    1200 sin 1200
    tan =
    2 1+cos 120 0

    √3
    2
    Ratio Identity =±
    −1
    1+( )
    2

    sinθ √3
    2. tanθ= = (2)
    cos θ 2
    1 1200
    tanθ= tan =√ 3
    cot θ 2

    Recall:

    cos θ
    cotθ=
    sinθ
    1
    tanθ = cos θ
    sin θ

    1 sin θ
    tanθ= ( )
    1 cos θ

    sinθ
    tanθ=
    cos θ

    tanθ=tan θ

    Pythagorean Identity

    1 sin2 θ cos 2 θ
    3. =
    sin2 θ sin 2 θ
    1 sin 2 θ cos2 θ
    == +
    sin2 θ sin 2 θ cos2 θ

    1
    Recall: = cscθ
    sin θ

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