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Unit 7 Lesson 4 Notes: The 3 Trigonometric Ratios Name Learning Targets: I CAN; 1) identify the sine, cosine, and tangent ratios of an acute angle of a right triangle. 2) set up sine, cosine, or tangent ratio proportions to solve for missing side lengths of right triangles.3) change calculator mode to degree mode and access the 3 trigonometric functions. VOCABULARY Trigonometric ratio Let ABC be a right triangle with acute A. The sine of A, cosine of A, and tangent of A (written sin A, cos A, and tan A) are defined as follows: Sine A, sin A = length of leg opposite = length of hypotenuse Cosine A, cos A = length of leg adjacent to = length of hypotenuse length of leg opposite A = length of leg adjacent to A Tangent A, tan A = In exercises 1 – 6, use MPQ at the right. 1. Name the side opposite M . _______________ 2. Name the side adjacent to M . _______________ 3. Name the side opposite Q . _______________ 4. Name the side adjacent to Q . _______________ Q M 5. Name the hypotenuse of MPQ . _______________ P 6. Name the acute angles of MPQ . _______________ Target 1 – Identify sine, cosine, and tangent ratios. Use the definitions of the three trigonometric ratios to complete each statement. 7. sin A = _______ 8. sin B = ________ 9. sin C = ________ cos A = _______ cos B = ________ cos C = ________ tan A = _______ tan B = ________ tan C = ________ R t o a T T Y r A B y O c e b C t E Find the sine, the cosine, and the tangent of A and B . Keep all answers in simplified fraction form! 10. B 11. C 10 B 12 5 12. 13 8 21 B 29 C 20 A C A 6 A A B A B A B Sine: ________ ________ Sine: ________ ________ Sine: ________ ________ Cosine: ________ ________ Cosine: ________ ________ Cosine: ________ ________ Tangent: ________ ________ Tangent: ________ ________ Tangent: ________ ________ Target 2 - Set up and solve sine, cosine, or tangent ratio proportions. First: identify which trig ratio to use in order to solve for the desired variable. Second: write this proportion with all the information provided in the diagram. Last: solve the proportion. Find the value of each variable in the diagram. Round to the nearest tenth.