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Understanding Trigonometric Functions: Sine, Cosine, and Tangent in Geometry

This lesson covers the essential trigonometric functions: sine, cosine, and tangent, as well as methods to find the measures of angles and sides in right triangles. Students will practice using radical forms and apply the Pythagorean theorem to calculate missing values. Key concepts include using the acronym SOHCAHTOA to remember the relationships between the angles and sides of triangles. Problem-solving examples will help illustrate how to find heights of objects using angles of elevation. Homework and class activities are included for practical application.

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Understanding Trigonometric Functions: Sine, Cosine, and Tangent in Geometry

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  1. Designed by: • Emily FreemanMcEachern High School2400 New Macland RdPowder Springs, GA  30127

  2. Session 17 Warm – up: Find the missing measures. Write all answers in radical form. 30° 45° x 7 10 z 45° w 60° y

  3. 13.4 & 13.5 The Trigonometric Functions we will be looking at SINE COSINE TANGENT

  4. The Trigonometric Functions SINE COSINE TANGENT

  5. SINE Prounounced “sign”

  6. COSINE Prounounced “co-sign”

  7. TANGENT Prounounced “tan-gent”

  8. Greek Letter q Prounounced “theta” Represents an unknown angle

  9. hypotenuse hypotenuse opposite opposite adjacent adjacent

  10. We need a way to remember all of these ratios…

  11. Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

  12. Sin SOHCAHTOA Opp Hyp Cos Adj Hyp Tan Opp Adj Old Hippie

  13. Finding sin, cos, and tan

  14. SOHCAHTOA 10 8 6

  15. Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6

  16. Find the values of the three trigonometric functions of . ? Pythagorean Theorem: 5 4 (3)² + (4)² = c² 5 = c 3

  17. Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). B 24.5 8.2 A 23.1

  18. Practice Workbook Page 77 # 1-4 Page 78 # 1-4

  19. Finding a side

  20. Ex. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? tan 71.5° ? tan 71.5° 71.5° y = 50 (tan 71.5°) 50 y = 50 (2.98868)

  21. Ex. 5 A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards

  22. Practice Workbook Page 77 # 7 & 8 Page 78 # 5 & 6

  23. Classwork: Worksheet SPW 147 & 149 due at the end of class.

  24. HOMEWORK: P. 568 # 8-12, 14, 17, 18 P. 576 # 12-15, 20-21, 22-32 even Quiz next class

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