Topic 11 Periodic and Exponential Functions I

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Topic 11 Periodic and Exponential Functions I. Recall A S T C. opp hyp. + +. sin θ = = = + cos θ = = = + tan θ = = = +. adj hyp. + +. θ. opp adj. + +. opp hyp. + +. sin θ = = = + cos θ = = = - tan θ = = = -. - PowerPoint PPT Presentation

Transcript of Topic 11 Periodic and Exponential Functions I

  • Topic 11

    Periodic and Exponential Functions I

  • RecallA S T C

  • sin= = = +

    cos= = = +

    tan= = = +

    opphyp++adjhyp++oppadj++

  • sin= = = +

    cos= = = -

    tan= = = -

    opphyp++adjhyp-+oppadj+-

  • sin= = = -

    cos= = = -

    tan= = = +

    opphyp-+adjhyp-+oppadj--

  • sin= = = -

    cos= = = +

    tan= = = -

    opphyp-+adjhyp++oppadj-+

  • ALL +COS +TAN +SIN +A S T Cllentralotations

  • ALL +COS +TAN +SIN +A S T Clllasseseachaints

  • ALL +COS +TAN +SIN +A S T CllonstantlyalkheilasBlah blah blah !!!!Yappity yappity

  • Sine of any angle

    Cosine of any angle

    Tangent of any angle

  • RecallA S T Ctan = sin / cos sin (90-) = cos cos (90-) = sin sin2 + cos2 =1sin, cos and tan of 30o , 60o and 45o

  • sin 30o = cos 30o =tan 30o = sin 60o =cos 60o = tan 60o = 3060

  • sin 45o = cos 45o =tan 45o = 1 4545

  • So we can express every trig ratio in terms of sin and cos

  • Model: Evaluate (a) cosec /4 (b) cot 5/3

  • Model: If sec = 5/4, find cot if is acute

    345

  • Model: Prove(a) cosec2x = sec x cosec x cot x(b) 1/(cosec x + 1) + 1/(cosec x -1) = 2tan x sec x

  • Model: Prove(a) cosec2x = sec x cosec x cot x(b) 1/(cosec x + 1) + 1/(cosec x -1) = 2tan x sec x