Algebra Trig Test 1 Review Key

Algebra 2 Honors Trig Test 1 Review Name: Key Date: 1. If sinθ = -2/3 and cosθ < 0, find the other five trig functions. No Calculator. sinθ = -2/3 cscθ = -3/2 cosθ = -√5/3 secθ = -3√5/5 tanθ = 2√5/5 cotθ = √5/2 Find the exact value for x and y. No calculator. 2. x = 5 3. x = 5√3 y = 10 4. x = 6√2 5. Find the perimeter of the triangle below. Perimeter = 6 + 6√2 + 6√2 = 6 + 12√2 = 18√2 Draw a picture for each! Round all answers to the nearest thousandth. You MAY NOT use Law of Sines or Law of Cosines for this section.   6. A woman standing on a hill sees a flagpole that she knows is 60 feet tall. The angle of depression from her line of sight to the bottom of the pole is 14°,   and the angle of elevation from her line of sight to the top of the pole is 18°. Find her distance from the pole. tan 18° = x/y y tan 18° = x tan 14° = (60 - x)/y y tan 14° = 60 - x y tan 18° = 60 - y tan 14° y tan 18° + y tan 14° = 60 y(tan 18° + tan 14°) = 60 y = 60 / (tan 18° + tan 14°) ≈ 104.485 feet 7. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle of 75° from the horizontal. An observer 600 m away on the other side of the cloud, measures the angle of elevation to the spot of light to be 45°. Find the height of the cloud cover. (600-x)tan75° = x 2239.23 - 3.73x = x 2239.23 = 4.73x x = 473.205 m 8. A trapezoid has bases 4 cm and 12 cm with base angles 30° and 60°. Find the perimeter (exactly). x√3 + x√3/3 + 4 = 12 4x√3/3 = 8 x√3 = 6 x = 2√3 Perimeter = 20 + 4√3 Find the sign of the expression if the terminal point determined by t is in the given quadrant. 9. cotθ csc²θ; QIII (-)(+) = - 10. tanθ secθ; QII (-)(-) = + From the information given, find the quadrant in which θ lies. 11. tanθ > 0 and sinθ < 0 QIII 12. cscθ > 0 and secθ < 0 QII Find the exact value of the function. No Calculator. 13. cos(π/2) 0 14. sin(2π/3) √3/2 15. sin(3π/4) √2/2 16. csc(7π/6) -2 17. tan(315°) -1 18. cos(10π/3) -1/2 Solve the following triangles using the Law of Sines or Cosines. Round answers to the nearest tenth. 19. A = 110°, a = 18, b = 12 sin110° / 18 = sinB / 12 B ≈ 38.8° C ≈ 31.2° c ≈ 9.9 20. A = 36°, a = 6, b = 8 sin36° / 6 = sinB / 8 B ≈ 51.6° C ≈ 92.4° c ≈ 15.6 21. a = 150°, b = 100, c = 200 b² = a² + c² - 2ac cos B 100² = 150² + 200² - 2(150)(200)cos B 22500 = 62500 - 60000cos B -40000 = -60000cos B cos B = 2/3 B ≈ 48.2° A ≈ 21.8° C ≈ 10° 22. a = 9, b = 10, c = 15 15² = 9² + 10² - 2(9)(10)cos C 225 = 181 - 180cos C 44 = -180cos C cos C = -11/45 C ≈ 104.1° B ≈ 40.3° A ≈ 35.6° Find the areas of the following triangles. Round answers to the nearest tenth. 23. A = 25°, B = 50°, b = 30 K = 1/2(30)²sin25°sin50° K ≈ 239.8 24. C = 45°, a = 18, b = 10 K = 1/2(18)(10)sin45° K ≈ 63.6 25. a = 7, b = 12, c = 8 K = √(13.5)(6.5)(1.5)(5.5) K ≈ 13.5 Solve the following. In the previous section, you HAD to use Right Triangles. In this section, you may use Right Triangles or the Laws of Sines and Cosines.   26. Two snowmobilers start from the same point and drive at   10 km/h and 12 km/h, respectively, diverging at an angle of 110°. Two hours after leaving, they find that their radio transmissions are barely audible. How far apart are they at that time? Round to the nearest thousandth.   x² = 20² + 24² - 2(20)(24)cos110° x² = 976 - 960cos110° x² ≈ 1304.4 x ≈ 36.116 km 27. Jan is flying a plane on a triangular course at 320 mi/h. She flies due east for two hours and then turns right through a 65°   angle. How long after turning will she be exactly southeast of where she started?   sin 20° / 640 = sin 45° / x x ≈ 1323.162828 ≈ 4 hours and 32 minutes 28. In quadrilateral ABCD, AB = 3, BC = 4, CD = 5, and DA = 6. The length of diagonal BD is 7. Find the length of the other diagonal. Round to the nearest tenth. 6² = 3² + 7² - 2(3)(7)cos x -22 = -42cos x x ≈ 58.41° 5² = 4² + 7² - 2(4)(7)cos y -40 = -56cos y y ≈ 44.42° AC² = 3² + 4² - 2(3)(4)cos102.83° AC² ≈ 30.329417 AC ≈ 5.5