3. Trigonometric Functions

Calculus 1



Weiqi Zhou


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Radian vs. Degrees

  • a full rotation is equally splitted into 360 degrees

  • the angle with unit arc length in a unit circle is defined to have 1 radian

  • a full rotation equals radian

  • positive radian/degree: measured counterclockwise
    negative radian/degree: measured clockwise

Trigonometry






Memorize the chart!

utterly important

Identities








Identities





Exercises

I will write down some trigonometric expressions on the board for you to compute their values

Properties

  • for :

  • -periodic and odd

  • bouned between and

  • attains maximum at ,
    attains minimum at ,

  • equals at ,

Properties

  • for :

  • -periodic and even

  • bouned between and

  • attains maximum at ,
    attains minimum at ,

  • equals at ,

Properties

  • for :

  • -periodic and odd

  • unbouned near

  • undefined at

  • equals at ,

Exercises

compute and where this year

Exercises

compute and for and respectively

Exercises

compute

Summary

  • Radians

  • Trigonometric functions and their properties

  • Trigonometric identities and the double angle formula