1. EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5 feet, and the length of the adjacent side is 12 feet. The length of the hypotenuse is 13 feet.

2. EXAMPLE 1 Finding Trigonometric Ratios sin P = hypotenuse opposite = 5 13 cos P hypotenuse adjacent = 12 13 = tan P adjacent opposite = = 5 12

3. EXAMPLE 2 Using a Calculator Use a calculator to find sine, cosine, and tangent of 30. ANSWER sin 30 0.5 = cos 30 0.8660 tan 30 0.5774 Display Keystrokes a. c. b.

4. GUIDED PRACTICE for Examples 1 and 2 sin A = hypotenuse opposite = 8 17 cos A hypotenuse adjacent = 15 17 = tan A adjacent opposite = = 8 15 1. For ABC, write the sine, cosine, and tangent ratios for A and C. Which ratio has a value greater than 1 ?

5. GUIDED PRACTICE for Examples 1 and 2 cos C = hypotenuse opposite = 8 17 tan C adjacent opposite = = 15 8 Tan c has a value greater than to 1 sin C = hypotenuse opposite = 15 17

6. GUIDED PRACTICE for Examples 1 and 2 2. Draw a 45 o –45 o –90 o triangle. Label the legs 2 ft and the hypotenuse appropriately. Write the sine, cosine, and tangent ratios for one of the 45 o angles. Does it make a difference which 45 o angle you choose? Explain. ANSWER

7. GUIDED PRACTICE for Examples 1 and 2 cos A = hypotenuse opposite = 1 2 tan A adjacent opposite = = 1 1 sin A = hypotenuse opposite = 1 2 It does not make a difference because the opposite and adjacent values are the same.

8. GUIDED PRACTICE for Examples 1 and 2 Use a calculator to approximate the expression. Round your answer to four decimal places. cos 75 o 3. ANSWER 0.3420 tan 50 o 4. ANSWER 1.1918

9. GUIDED PRACTICE for Examples 1 and 2 Use a calculator to approximate the expression. Round your answer to four decimal places. sin 25 o 5. ANSWER 0.4226 tan 7 o 6. ANSWER 0.1228