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Extending Trigonometric Ratios: Reciprocal Functions and Unit Circle Concepts

This lesson focuses on extending trigonometric ratios, specifically the reciprocal trig functions such as secant, cosecant, and cotangent. Students will solve triangles and explore the unit circle, defining sine and cosine in terms of rotational angles. With exercises that include sketching angles like 150° and 210°, and finding specific coordinates on the unit circle, learners will enhance their understanding of trigonometric concepts. Assignments are provided to reinforce these topics through practice problems and graphical analysis.

elisabeth-newton
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Extending Trigonometric Ratios: Reciprocal Functions and Unit Circle Concepts

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  1. 10.3 Extending the Trigonometric Ratios Warm up 1. Solve the triangle A c 12 C B 15

  2. Section 10-3 Reciprocal Trig Ratios

  3. 1. Sketch 150°

  4. 2. Sketch 210°

  5. 10.3 Extending the Trigonometric Ratios Reciprocal Trig Function

  6. 3. Find sec A B 11 3 C A 7

  7. 10.3 Extending the Trigonometric Ratios Definitions Unit Circle Definition of Sine and Cosine: Let  be a rotational angle. Then sin  is the y-coordinate of the image of the point P(1, 0) rotated  ° about the origin, and cos  is the x-coordinate. θ

  8. 10.3 Extending the Trigonometric Ratios 4. Find the coordinates of point P on the unit circle. Point P has coordinates (cos 120, sin 120)  (–0.5, 0.8660).

  9. Assignment Enrichment 8-5 and page 652 # 13-32 # 21-28 are graphs and # 29 – 32 are find sine and cosine

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