1. www.thevisualclassroom.com Trigonometry: The study of triangles (sides and angles) physics surveying Trigonometry has been used for centuries in the study of: astronomy geography engineering

2. www.thevisualclassroom.com A B C adjacent h y p o t e n u s e opposite

3. A B C adjacent opposite h y p o t e n u s e

4. A B C opposite adjacent h y p o t e n u s e

5. A B C opposite adjacent h y p o t e n u s e

6. A B C opp adj hyp SOHCAH TOA

7. www.thevisualclassroom.com A B C 8 6 10 op p adj hy p SOH CAH TOA

8. www.thevisualclassroom.com A B C 3 4 5 adj opp hyp SOH CAH TOA

9. www.thevisualclassroom.com A B C 5 12 13 adj opp hy p SOH CAH TOA

10. www.thevisualclassroom.com sin 21° = cos 53° = tan 72° = 0.3584 0.6018 3.0777 Use a calculator to determine the following ratios.

11. www.thevisualclassroom.com sin A = 0.4142 cos B = 0.6820 tan C = 1.562  A = sin -1 (0.4142)  B = cos -1 (0.6820)  C = tan -1 (1.562) = 24° = 47° = 57° Determine the following angles (nearest degree).

12. www.thevisualclassroom.com Determine the following angles (nearest degree). sin A = cos B = tan C =  A = sin -1 (0.5833)  B = cos -1 (0.2666)  C = tan -1 (1.875) = 36° = 75° = 62° = 0.5833 = 0.2666 = 1.875

13. www.thevisualclassroom.com A B C a 6 cm Example 1: Determine side a 30º a = 6 sin 30° a = 3 cm a = 6 (0.5) hyp opp SOH CAH TOA

14. www.thevisualclassroom.com A B C 50º b 9 m 40º Ex. 2: Name two trig ratios that will allow us to calculate side b.

15. www.thevisualclassroom.com A B C Example 3: Determine side b 55º b 8 cm b = 8 tan 55° b = 11.4 cm b = 8 (1.428) opp ad j SOH CAH TOA

16. www.thevisualclassroom.com P Q R 12 cm 17 cm Example 4: Determine the measure of  P. cos P = 0.70588  P = 45.1   P = cos –1 (0.70588) adjacent hypotenuse SOH CAH TOA

17. www.thevisualclassroom.com P Q R q 12 cm Example 5: Determine the measure of side PR. q(tan 35°) = 12 q = 17.1 cc m 35  opp adj Method 1

18. www.thevisualclassroom.com P Q R q 12 cm Example 6: Determine the measure of side PR. q = 12(tan 55°) q = 17.1 cc m 35  opp adj Method 2  Q = 90° – 35°  Q = 55° 55° q = 12(1.428)

19. www.thevisualclassroom.com Ex. 7: In  PQR,  Q = 90°. a) Find sin R if PR = 8 cm and PQ = 4 cm. R P Q 4 cm 8 cm b) Find cos R. RQ 2 = 8 2 – 4 2 RQ 2 = 64 – 16 RQ 2 = 48