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Main Ideas of Adv PreCalc Ch. 4 Class 1

Main Ideas of Adv PreCalc Ch. 4 Class 1. Positive Negative Angles in X-Y Plane Radian Radian – Degree Conversion 70 o to radians (leave in terms of ) to degrees Quadrants Arc measure Linear Speed Angular Speed Degrees, Minutes, Seconds Conversion (DMS).

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Main Ideas of Adv PreCalc Ch. 4 Class 1

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  1. Main Ideas of AdvPreCalc Ch. 4 Class 1 Positive Negative Angles in X-Y Plane Radian Radian – Degree Conversion 70o to radians (leave in terms of ) to degrees Quadrants Arc measure Linear Speed Angular Speed Degrees, Minutes, Seconds Conversion (DMS)

  2. Main Ideas of AdvPreCalc Ch. 4 Class 2 Six Trigonometric Functions 30-60-90 Triangles 45-45-90 Triangles Sin, Cos, Tan of Special Angles Complementary and Supplementary Angles (in degrees and radians) Cofunctions of complementary angles sin(90o – ө) = cos(ө) cos(90o – ө) = sin(ө) tan(90o – ө) = cot(ө) sec(90o – ө) = csc(ө) csc(90o – ө) = sec(ө) cot(90o – ө) = tan(ө)

  3. Main Ideas of AdvPreCalc Ch. 4 Class 3 Six Trigonometric Functions in X-Y Plane, on Unit Circle Trigonometric Functions for any size Circle Fundamental Trigonometric Identities Pythagorean Identities Applying Trigonometric Identities Applications

  4. Main Ideas of Adv PreCalc Ch. 4 Class 4 Reference Angles Trigonometric Functions of any Angle Find Reference Angle Determine Trig. Functions for that reference angle Locate correct Quadrant to determine positive or negative sign

  5. Main Ideas of AdvPreCalc Ch. 4 Class 5 Graph sin and cos functions: y = a sin bx, y = a cosbx Identify Amplitude: a Period = Translations: y = a sin(bx – c) + k Set (bx – c) = 0 and solve for x (left end of one cycle) Set (bx – c) = 2solve for x (right end of one cycle) Locate ¼, ½, and ¾ interval points Move up or down k units

  6. Main Ideas of AdvPreCalc Ch. 4 Class 6 Graph tan function: y = a tan bx Period = Vertical Asymptotes: Graph cot function: y = a cot bx Period = Vertical Asymptotes: Translations Graph sec and csc functions: use cos and sin graph Damped sin and cos graphs: y = e-x sin2x

  7. Main Ideas of AdvPreCalc Ch. 4 Class 7 Inverse sin, cos, and tan: sin-1 t = arcsin t Domain of arcsin and arctan: -, + Domain of arccos: 0,

  8. Main Ideas of AdvPreCalc Ch. 4 Class 8 Composition of Trigonometric Functions sin and arcsin are inverses sin(arcsin t) = t, and arcsin(sin t) = t, if t in domain of sin and arcsin Similarly for cos and arccos, and tan and arctan

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