Section 4.4 handout ann_1

Section 4.4 handout ann_1 - Section 4.4 Trigonometric...

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Section 4.4 Trigonometric Functions of Any Angle, Page 1 Section 4.4 Trigonometric Functions of Any Angle, Page 1
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Section 4.4 Trigonometric Functions of Any Angle, Page 2 Section 4.4: Trigonometric Functions of Any Angle 1) Definitions: The Trigonometric Functions of Any Angle . a. If P ( x , y ) is a point on the terminal side of θ , an angle whose vertex is at the origin, then the trigonometric functions  are defined as: sin θ = y / r csc θ = r / y cos θ = x / r sec θ = r / x tan θ = y / x cot θ = x / y where r = ( x 2 + y 2 ) 1/2 b. Example 1 : Let P ( x, y ) = (–5, 7), find sin θ . Step 1 . Find r using the Pythagorean Theorem. Step 2 . Find sin θ using the definitions above. 2) The Signs of Trigonometric Functions . a. Since sin θ = y/r , the sign of sin θ depends on the sign of y .  Sin θ  is positive when y i s positive and negative when  y is negative. b. Since cos θ = x/r , the sign of cos θ depends on the sign of x .  Cos θ  is positive when x is positive and negative when  x is negative.
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