1. 9-2 Sine and Cosine Ratios

2. There are two more ratios in trigonometry that are very useful when determining the length of a side or the measure of an angle. A B C length of leg opposite  A sine of  A = -------------------------------- length of hypotenuse length of leg adjacent  A cosine of  A = -------------------------------- length of hypotenuse

3. Sine A B C length of leg opposite  A sine of  A = -------------------------------- length of hypotenuse opposite sinA = ----------- hypotenuse

4. What is the sine of 45  ? A B C 45  2 2 opposite 2 sinA = sin45  = ----------- = ---- = ?? hypotenuse ?? opposite 2 sinB = sin45  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the sine of 45  ? All 45  angles have a sine of.7071 (  2 / 2).

5. What is the sine of 60  ? A B C 60  ?? 1 opposite ?? sinA = sin60  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the sine of 60  ? All 60  angles have a sine of.8660 (  3/2 ).

6. What is the sine of 30  ? A B C 60  ?? 1 opposite ?? sinB = sin30  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the sine of 30  ? All 30  angles have a sine of.5 (1/2 ).

7. Cosine A B C length of leg adjacent  A cosine of  A = -------------------------------- length of hypotenuse adjacent cosA = ----------- hypotenuse

8. What is the cosine of 45  ? A B C 45  2 2 adjacent 2 cosA = cos45  = ----------- = ---- = ?? hypotenuse ?? adjacent 2 cosB = cos45  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the cosine of 45  ? All 45  angles have a cosine of.7071 (  2 / 2).

9. What is the cosine of 60  ? A B C 60  ?? 1 adjacent ?? cosA = cos60  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the cosine of 60  ? All 60  angles have a cosine of.5 (1/2 ).

10. What is the cosine of 30  ? A B C 60  ?? 1 adjacent ?? cosB = cos30  = ----------- = ---- = ?? hypotenuse ?? Look at the trig table on page 731. What is the cosine of 30  ? All 30  angles have a cosine of.8660 (  3/2 ).

11. Note: (verify these with your calculator or p. 731) sin 45 = cos 45 sin 30 = cos 60 sin 60 = cos 30 sin 55 = cos ?? sin11 = cos ?? What can you conclude? sinA = cosB where A + B = 90

12. S O H C A H T O A I N E P P O S I T E P P O S I T E O S I N E A N G E N T Y P O T E N U S E Y P O T E N U S E D J A C E N T D J A C E N T

13. Give the sine and cosine ratios for angles A and B.

14. Use your calculator, or the trig table, to determine a missing side of a right triangle. Instead of using the tan button, use sin or cos.

15. Find the value of x, to the nearest tenth.

16. Find the value of x to the nearest degree.

17. Remember: S O H C A H T O A

18. Homework: p. 479 1 - 17, 22 - 24