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6.3: Trig. Functions of Angles

6.3: Trig. Functions of Angles.

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6.3: Trig. Functions of Angles

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  1. 6.3: Trig. Functions of Angles TSW be able to find the reference angle for a given angle, be able to apply the reference angle to evaluate trigonometric functions, and understand and be able to apply the Pythagorean and reciprocal identities of the trigonometric functions at an 85% mastery level as demonstrated by discussion and practice.

  2. Definition Let θbe an angle in standard position. If is the distance from the origin to the point P(x, y), then r y x

  3. Finding Trig. Functions Ex: Find a. cos 135o b. tan 390o Ex: Find the reference angle for a. b. Ex: Use the reference angle to evaluate: a. b. c. d.

  4. Using Trig. Identities Ex: Express sinθ in terms of cosθ. Ex: Express tanθ in terms of sinθ, where θ is in quadrant II. Ex: If tanθ = ⅔ and θ is in quadrant III, find cosθ. Ex: If secθ = 2 and θ is in quadrant IV, find the other five trigonometric functions of θ.

  5. Area of a Triangle The area of a triangle with sides of lengths a and b and with included angle θ is Ex: Find the area of triangle ABC shown. C 3 cm A B 10 cm

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