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    Trigo 2

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    Julie Ocol
    Trigonometry involves defining trigonometric functions like sine, cosine, and tangent for angles and using identities and formulas to relate them. Key concepts include the right triangle definition of trig functions, Pythagorean identities, sum and difference formulas, double angle formulas, inverse trig functions, and laws relating trig functions of angles in triangles. Trigonometry has applications in many areas of mathematics, science, and engineering.

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    Trigo 2

    Uploaded by

    Julie Ocol
    169 views2 pages
    Trigonometry involves defining trigonometric functions like sine, cosine, and tangent for angles and using identities and formulas to relate them. Key concepts include the right triangle definition of trig functions, Pythagorean identities, sum and difference formulas, double angle formulas, inverse trig functions, and laws relating trig functions of angles in triangles. Trigonometry has applications in many areas of mathematics, science, and engineering.

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    trigo

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    trigo 2

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    Trigonometry involves defining trigonometric functions like sine, cosine, and tangent for angles and using identities and formulas to relate them. Key concepts include the right triangle definition of trig functions, Pythagorean identities, sum and difference formulas, double angle formulas, inverse trig functions, and laws relating trig functions of angles in triangles. Trigonometry has applications in many areas of mathematics, science, and engineering.

    Copyright:

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

    Trigo 2

    Uploaded by

    Julie Ocol
    Trigonometry involves defining trigonometric functions like sine, cosine, and tangent for angles and using identities and formulas to relate them. Key concepts include the right triangle definition of trig functions, Pythagorean identities, sum and difference formulas, double angle formulas, inverse trig functions, and laws relating trig functions of angles in triangles. Trigonometry has applications in many areas of mathematics, science, and engineering.

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    Trigonometry

    Reciprocal Identities Half Angle Formulas


    1 1 1
    cscθ = sinθ = θ 1-cosθ sin²θ = (1-cos(2θ))
    sinθ cscθ sin =±√ 2
    1 1 2 2
    secθ = cosθ =
    Right Triangle Definition cosθ secθ 1
    1 1 θ 1+cosθ cos²θ = (1+cos(2θ))
    For this definition we assume that 0<θ cos =±√ 2
    π cotθ = tanθ = 2 2
    < 2 or 0°< θ <90° tanθ cotθ
    1-cos(2θ)
    Pythagorean Identities θ 1-cosθ tan²θ =
    tan =±√ 1+ cos (2θ)
    sin²θ + cos²θ = 1 2 1+cosθ
    tan²θ + 1 = sec² θ
    1 + cot²θ = csc²θ Sum and Difference Formulas
    sin(α±β) = sinαcosβ±cosαsinβ
    Even/Odd Formulas cos(α±β) = cosαcosβ∓sinαsinβ
    opposite hypotenuse sin(-θ) = -sinθ csc(-θ) = -cscθ tan α ± tan β
    sinθ = cscθ = tan(α±β) =
    hypotenuse opposite cos(-θ) = cosθ sec(-θ) = secθ 1∓ tan α tan β
    adjacent hypotenuse
    cosθ = secθ = tan(-θ) = -tanθ cot(-θ) = -cotθ
    hypotenuse adjacent Product to Sum Formulas
    opposite adjacent 1
    tanθ = cotθ = Periodic Formulas
    adjacent opposite sinαsinβ= [cos(α-β)-cos(α+β)]
    If n is an integer. 2
    sin(θ+2πn) = sinθ csc(θ+2πn) = cscθ 1
    Unit circle definition cosαcosβ= [cos(α-β)+cos(α+β)]
    cos(θ+2πn) = cosθ sec(θ+2πn) = secθ 2
    For this definition θ is any angle. 1
    tan(θ+πn) = tanθ cot(θ+πn) = cotθ sinαcosβ= [sin(α+β)+sin(α-β)]
    2
    Double Angle Formulas 1
    cosαsinβ= [sin(α+β)-sin(α-β)]
    sin(2θ) = 2sinθcosθ 2
    cos(2θ) = cos²θ-sin²θ
    Cofunction Formulas
    = 2cos²θ-1 π π
    =1-2sin²θ sin ( -θ) = cosθ cos ( -θ) = sinθ
    2 2
    2tanθ π π
    y 1 tan(2θ)= csc ( -θ) = secθ sec ( -θ) = cscθ
    sinθ = =1 cscθ = 1-tan²θ 2 2
    1 y π π
    x 1 tan ( -θ) = cotθ cot ( -θ) = tanθ
    cosθ = = 1 secθ = Degrees to Radians Formulas 2 2
    1 x
    y x If x is an angle in degrees and t is an
    tanθ = cotθ = angle in radians then
    x y
    π t πx 180t
    = ⇒ t= and x =
    180 x 180 π

    Definition
    y=sin-1x is equivalent to x=siny
    y=cos-1x is equivalent to x=cosy
    Tangent and Cotangent Identities
    sinθ cosθ y=tan-1x is equivalent to x=tany
    tanθ = cotθ =
    cosθ sinθ
    Domain and Range Law of Tangents
    Function Domain Range 1
    π π a-b tan 2 (α-β)
    Y=sin-1x -1≤ x ≤1 - ≤y≤ =
    2 2 a+b tan 1 (α+β)
    Y=cos-1x -1≤ x ≤1 0≤ y ≤π 2
    Y=tan-1x -∞≤ x π π 1
    - ≤y≤ b-c tan 2 (β-γ)
    ≤∞ 2 2 =
    b+c tan 1 (β+γ)
    2
    Inverse Properties 1
    cos(cos-1(x)) = x cos-1(cos(θ)) = θ a-c tan 2 (α-γ)
    =
    sin(sin-1(x)) = x sin-1(sin(θ)) = θ a+c tan 1 (α+γ)
    Law of Sines 2
    tan(tan-1(x)) =x tan-1(tan(θ)) = θ sinα sinβ sinγ
    = =
    a b c Mollweide’s Formula
    Alternate Notation 1
    sin-1x = arcsinx a+b cos 2 (α-β)
    Law of Cosines =
    cos-1x = arccosx a2=b2+c2-2bccosα c 1
    sin γ
    tan-1x = arctanx 2
    b2=a2+c2-2accosβ
    c2=a2+b2-2abcos𝛾

    For any ordered pair on the unit circle ( x y, ) : cosθ= x and sinθ = y

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