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MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions. Section 1 - Trigonometric Functions of Acute Angles. IN. Function Machine. OUT. Review: Functions & Functional Notation. Definition

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MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions

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  1. MTH 112Elementary FunctionsChapter 5The Trigonometric Functions Section 1 - Trigonometric Functions of Acute Angles

  2. IN Function Machine OUT Review: Functions & Functional Notation • Definition • A association between one or more sets of elements (domain) and a unique element in another set (range). • Notation • functionName(parameters) = functionDefinition • Examples • age(person) = number of years on earth • add(a,b) = a + b • f(x) = x2 + 5x - 3

  3. Hypotenuse Side Opposite Angle   Side Adjacent to Angle  Parts of a Right Triangle

  4. Hypotenuse Side Adjacent to Angle  Side Opposite Angle  Parts of a Right Triangle

  5. sine of  sin() = opp / hyp cosine of  cos() = adj / hyp tangent of  tan() = opp / adj cosecant of  csc() = hyp / opp secant of  sec() = hyp / adj cotangent of  cot() = adj / opp hyp opp  adj Defining the Trig Functions of an Acute Angle  of a Right Triangle

  6. H O  A Memory Aids: Trig Function Definitions Oscar Had AHeap Of Apples. O = opposite A = adjacent H = hypotenuse sin  = O/H cos  = A/H tan  = O/A SOHCAHTOA Sin = Opp / Hyp; Cos = Adj / Hyp; Tan = Opp / Adj

  7. 10 6 5 3  4 8 Are the values of the trig functions dependent on the triangle or just the angle? Why? Ratios of corresponding sides of similar triangles are equal.

  8. Given one of the trig values of an acute angle of a right triangle, can you find the other 5 trig values of that angle? • Write the given value as a fraction. • Label a triangle with the known values. • Find the third side using the Pythagorean theorem. • Use the definitions to find the other 5 trig function values.

  9. Reciprocal Trig Functions • Note that your calculator only provides three of the trig functions. Why? • From the definitions, we have the following relationships. • csc  = 1 / sin  • sec  = 1 / cos  • cot  = 1 / tan  • Is there a difference between sin  and sin()?

  10. 90°- c b  a Cofunction Identities • sin  = cos(90°- ) • tan  = cot(90°- ) • sec  = csc(90°- ) • cos  = sin(90°- ) • cot  = tan(90°- ) • csc  = sec(90°- ) What is the relationship between a trig function and its co-trig function? Compare a trig value of an angle and the co-trig value of the complementary angle.

  11. x 45° x Trig Values of a 45° Angle

  12. x x 60° x Trig Values of a 60° Angle x / 2

  13. x x 60° x / 2 Trig Values of a 30° Angle 30°

  14. Trig Values of any Acute Angle • Measuring Angles: • DMS vs. decimal degrees vs. radians • Calculator mode settings for angle measurement. • Using a Calculator to find Trig Values • Results are approximations! • What about sec, csc, and cot? • Using a Calculator to find the angle given a trig value.

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