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Trigonometric Ratios in Right Triangles

Trigonometric Ratios in Right Triangles. Section 5.2. Terminology/Notation. How are angles labeled? How are sides labeled?. Adjacent Side. The side that forms the angle that is not the hypotenuse. Name the adjacent side for angle B and angle A. Opposite Side.

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Trigonometric Ratios in Right Triangles

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  1. Trigonometric Ratios in Right Triangles Section 5.2

  2. Terminology/Notation • How are angles labeled? • How are sides labeled?

  3. Adjacent Side • The side that forms the angle that is not the hypotenuse. • Name the adjacent side for angle B and angle A.

  4. Opposite Side • The side that is directly across from the given angle. • Name the opposite side for angle B and angle A.

  5. Hypotenuse • The longest side of a right triangle. It is always the side opposite the 90° angle. • What is the hypotenuse of the triangle?

  6. Trigonometric Ratios • sin A = • cos A = • tan A =

  7. What about angle B? • sin B = • cos B = • tan B =

  8. Example 1 • Find the values of the sine, cosine and tangent for ∠ A.

  9. Reciprocal Trigonometric Ratios

  10. Example 2 • If sec A = , find cosA. • If sin B = 0.8 , find csc B.

  11. Example 3 • Find the values of the six trigonometric ratios for ∠E.

  12. Example 4 • Sketch a right triangle that has cosA = 3/5. • Find the following ratios a) sin A b) tan A c) csc A d) sec A e) cot A

  13. Example 5 • Use a calculator to find each expression to three decimal places a) sin 75° b) cos 10° c) sec 15° d) sin 45°12’13’’

  14. Special Right Triangles • 30°-60°-90° • Be able to draw and label this triangle from memory!!!

  15. Special Right Triangles • 45°-45°-90° • Be able to draw and label this triangle from memory!!!

  16. Example 6 • Complete the table:

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