Trig Part 1 Final Exam Review Key

Advanced Math Final Exam Review Packet Trig Part 1 Fill in the ratios for each trig function using the letters for opposite (O), adjacent (A) and hypotenuse (H) sin = O/H cos = A/H tan = O/A csc = H/O sec = H/A cot = A/O Find each value. No decimals, reduce fractions. 1. sin D = 3/5 2. sin E = 4/5 3. cot E = 3/4 4. tan D = 3/4 5. cos D = 4/5 6. csc D = 5/3 7. sec D = 5/4 8. cot D = 4/3 9. cos E = 3/5 10. tan E = 4/3 11. sec E = 5/3 12. csc E = 5/4 Using the 30-60-90 and 45-45-90 rules, find each length or angle measure. Express all lengths in simplest radical form. 13. AB = 6√2, BC = 6, MN = 15√2 14. AC = 12√3, AB = 12, ST = 5√2, TV = 5√2 15. BC = 18√3, AB = 18, MN = 10, ST = 5√2 Fill in the missing sides of the special right triangles and answer the following questions. Exact answers ONLY! sin 30° = 1/2 cos 30° = √3/2 tan 30° = √3/3 sin 45° = √2/2 cos 45° = √2/2 tan 45° = 1 sin 60° = √3/2 cos 60° = 1/2 tan 60° = √3 1   Use SOH CAH TOA to solve each problem. 25. Katlyn leans a 16-foot ladder against a wall. If the ladder makes an angle of 70° with the ground, how far up the wall does the ladder reach? sin(70°) = x/16 x = 16 * sin(70°) x ≈ 15.04 ft 26. Tom leans a 20-ft ladder against a wall. The base of the ladder is 4 feet from the wall. What angle does the ladder make with the ground? cos(θ) = 4/20 θ = cos⁻¹(4/20) θ ≈ 78.46° Find the reference angle for each: 27. 27° 28. 132° (180° - 132° = 48°) 29. 209° (209° - 180° = 29°) 30. 289° (360° - 289° = 71°) 31. Find the value of a to the nearest degree. [Image of a right triangle with sides 3 and 4] tan(a) = 4/3 a ≈ 53° 32. A school flagpole casts a 16-foot shadow on the lawn. A teacher stood at the shadow's edge and measured the angle of elevation to the top of the pole at 42°. How tall is the pole? [Image of a right triangle with height h and base 16] tan(42°) = h/16 h = 16 * tan(42°) h ≈ 14.4 ft 33. Find the value of j rounded to the nearest tenth. [Image of a right triangle with hypotenuse 51 and angle 75°] cos(75°) = j/51 51 * cos(75°) = j j ≈ 13.2 ft 34. Change 4π/3 to degrees. (4π/3) * (180°/π) = 240° 35. Determine the exact value of sin 150°. sin(150°) = sin(30°) = 1/2 36. Find the exact value of sec(2π/3). sec(2π/3) = sec(120°) = -2 37. Point P(0.8, 0.6) is located on a unit circle. Find sinθ and cosθ. sinθ = 0.6 cosθ = 0.8