EXAMPLE 1

1. Evaluate the six trigonometric functions of the angle θ. From the Pythagorean theorem, the length of the hypotenuse is √ 169 13. √ 52 + 122 = = opp hyp 13 12 sinθ cscθ = = = = 12 hyp opp 13 EXAMPLE 1 Evaluate trigonometric functions SOLUTION

2. 5 13 adj hyp cosθ secθ = = = = 13 5 hyp adj 12 5 opp adj tanθ cotθ = = = = 5 12 adj opp EXAMPLE 1 Evaluate trigonometric functions

3. Draw: a right triangle with acute angle θ such that the leg opposite θ has length 4 and the hypotenuse has length 7. By the Pythagorean theorem, the length xof the other leg is x = 33. √ 72 – 42 √ = EXAMPLE 2 Standardized Test Practice SOLUTION STEP 1

4. opp 4 33 4 tanθ = = = adj √ 33 33 ANSWER The correct answer is B. √ EXAMPLE 2 Standardized Test Practice Find the value of tan θ. STEP 2

5. 1. adj hyp 4 5 cosθ secθ = = = = 5 4 hyp adj opp adj 3 4 tanθ cotθ = = = = adj opp 4 3 opp hyp 3 5 sinθ cscθ = = = = hyp opp 5 3 for Examples 1 and 2 GUIDED PRACTICE Evaluate the six trigonometric functions of the angle θ. ANSWER

6. adj hyp 8 17 cosθ secθ = = = = 17 8 hyp adj opp adj 15 8 tanθ cotθ = = = = adj opp 8 15 opp hyp 15 17 sinθ cscθ = = = = hyp opp 17 15 for Examples 1 and 2 GUIDED PRACTICE Evaluate the six trigonometric functions of the angle θ. ANSWER

7. adj hyp 5 √ 5 2 cosθ secθ = = = = hyp adj 5 √ 5 2 opp adj 5 5 tanθ cotθ = = = = adj opp 5 5 opp hyp 5 √ 5 2 sinθ cscθ = = = = hyp opp 5 √ 5 2 for Examples 1 and 2 GUIDED PRACTICE Evaluate the six trigonometric functions of the angle θ. ANSWER = 1 = 1

8. In a right triangle, θ is an acute angle and cos θ= . What is sinθ? 4. ANSWER 7 10 51 sinθ = 10 √ for Examples 1 and 2 GUIDED PRACTICE