Trig Ratios in Right Triangles
Similar Triangles   If two angles of a triangle are congruent    to two angles of another triangle, the    triangles are ...
B            ca    C           A        b
B      Leg The side                    Hypotenuseadjacent to angle B    and opposite angle A          C              Leg  ...
Sine of angle A              B                  sin A = leg opposite                                       hypotenuse     ...
Cosine of angle A              B                  cos A = leg adjacent                                       hypotenuse   ...
Tangent of angle A              B                  tan A = leg opposite                                       leg adjacent...
Sine of angle B              B                  sin B = leg opposite                                       hypotenuse     ...
Cosine of angle B              B                  cos B = leg adjacent                                       hypotenuse   ...
Tangent of angle B              B                  tan B = leg opposite                                       leg adjacent...
SOHCAHTO   A
Trig Ratios in Right Triangles   sine θ        cosecant θ   cosine θ       secant θ   tangent θ       cotangent θ
Trig Ratios in Right Triangles    Words        Symbols      Definitioncosecant θ    csc θ        csc θ =                  ...
Find all six trigonometricfunctions of the angle θ.      8                 θ
Answers
Evaluate the remainingtrigonometric functions.
Answers
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Lesson 4.2

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Lesson 4.2

  1. 1. Trig Ratios in Right Triangles
  2. 2. Similar Triangles If two angles of a triangle are congruent to two angles of another triangle, the triangles are similar. If an acute angle of one right triangle is congruent to an acute angle of another right triangle, the triangles are similar, and the corresponding ratios are equal. Any two congruent angles of different right triangles will have equal ratios associated with them.
  3. 3. B ca C A b
  4. 4. B Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  5. 5. Sine of angle A B sin A = leg opposite hypotenuse Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  6. 6. Cosine of angle A B cos A = leg adjacent hypotenuse Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  7. 7. Tangent of angle A B tan A = leg opposite leg adjacent Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  8. 8. Sine of angle B B sin B = leg opposite hypotenuse Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  9. 9. Cosine of angle B B cos B = leg adjacent hypotenuse Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  10. 10. Tangent of angle B B tan B = leg opposite leg adjacent Leg The side Hypotenuseadjacent to angle B and opposite angle A C Leg A The side adjacent to angle A and opposite angle B
  11. 11. SOHCAHTO A
  12. 12. Trig Ratios in Right Triangles sine θ cosecant θ cosine θ secant θ tangent θ cotangent θ
  13. 13. Trig Ratios in Right Triangles Words Symbols Definitioncosecant θ csc θ csc θ = 1 sinsecant θ sec θ sec θ = 1 coscotangent θ cot θ cot θ = 1 tan
  14. 14. Find all six trigonometricfunctions of the angle θ. 8 θ
  15. 15. Answers
  16. 16. Evaluate the remainingtrigonometric functions.
  17. 17. Answers

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