1. 8 – 6 The Sine and Cosine Ratios

2. Sine and Cosine Suppose you want to fine the legs, x and y, in a triangle. You can’t find these values using the tangent ratio because the only side you know it the hypotenuse. The ratios that relate are sine and cosine. Sine = Cosine = hypotenuse Opposite leg Adjacent Leg

3. Sine and Cosine We now have 3 useful trigonometric ratios given below Tan A = Sin A = Cos A = SOHCAHTOA

4. Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

5. Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

6. Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

7. Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

8. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120 67 y x

9. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

10. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

11. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

12. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

13. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120(0.3907) = y 110.46 or 110 = x 120 67 y x

14. Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120(0.3907) = y 110.46 or 110 = x y = 46.884 or 47 120 67 y x

15. Sine and Cosine Find the value of n to the nearest integer 40 22 n o

16. Sine and Cosine Find the value of n to the nearest integer 40 22 n o

17. Sine and Cosine Find the value of n to the nearest integer 40 22 n o

18. Sine and Cosine Find the value of n to the nearest integer 40 22 n o

19. Sine and Cosine Find the value of n to the nearest integer 40 22 n o

20. Sine and Cosine Find the value of n to the nearest integer N = 33 40 22 n o