Lesson_7.1_Equivalent.trig.fns

Lesson_7.1_Equivalent.trig.fns -...

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Lesson_7.1_Equivalent.Trig.Fns 1 November 20, 2008 Chapter 7 - Trigonometric Identities and Trig Equations 7.1 - Equivalent Trig Functions Related Functions with π and 2 π Consider the four points separately and the primary trig ratios of the angles formed by the terminal arm as shown in the diagrams. θ θ θ θ cos( π - θ ) =-cos θ sin( π - θ ) = sin θ tan( π - θ ) =-tan θ cos( π + θ ) =-cos θ sin( π + θ ) = -sin θ tan( π + θ ) = tan θ cos(2 π - θ ) = cos θ sin(2 π - θ ) = -sin θ tan(2 π - θ ) = -tan θ cos θ = x/r sin θ = y/r tan θ = y/x Rules for simplifying If θ is measured from the x-axis, ie π or 2 π , keep the trig ratio use the CAST rule for the +/- sign Example 1 Simplify as a trig ratio of θ. a) tan( π - θ ) b) cos (2 π - θ) c) sin( π+θ) Example 2 If cos θ = , and 0< θ < a) cos( π + θ ) b) cos (2 π - θ ) c) sin( π + θ ) d) tan( π - θ ) Do sheet #1abcjkl, 3abe, 4ace
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Lesson_7.1_Equivalent.Trig.Fns 2 November 20, 2008 θ θ θ θ
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