1. Find the missing measures. Write all answers in radical form. 45° x w 7 60° 30° 10 y z

2. The Trigonometric Functions we will be looking at SINE COSINE TANGENT

3. The Trigonometric Functions SINE COSINE TANGENT

4. SINE Prounounced “sign”

5. Prounounced “co-sign” COSINE

6. Prounounced “tan-gent” TANGENT

7. Prounounced “theta” Greek Letter  Represents an unknown angle

8. opposite hypotenuse adjacent hypotenuse opposite adjacent

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

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

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

12. Finding sin, cos, and tan

13. 6 8 10 SOHCAHTOA

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

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

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

17. Let’s find the calculator connections. Draw a 30º-60º-90º to help you find sin 30º. Now use your calculator to find sin 30º. So… What is sin 45º? What is cos 27º? What is tan 62º? 1.8910 1.881

18. Can using the calculator help us solve this problem? In triangle PQR, m  P = 90º, and m  Q = 35º. If PQ = 16, find the lengths of the other two sides.

19. Can using the calculator help us solve this problem? In triangle PQR, m  P = 90º, and m  Q = 35º. If PQ = 16, find the lengths of the other two sides. Q 16 P R 35

20. Can using the calculator help us solve this problem? In triangle PQR, m  P = 90º, and m  Q = 35º. If PQ = 16, find the lengths of the other two sides. Q 16 P R 35

21. What about indirect measurement? The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite actually flying?

22. Solution: The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite flying? 100’ 79º h

23. 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? 50 71.5° x tan 71.5° x = 50 (tan 71.5°) x = 50 (2.98868) You try….

24. 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? 200 x 60° cos 60° x (cos 60°) = 200 x X = 400 yards