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Name ________________________________ 5.4-5.5 Review Test Info 50 points Part 1 – 30 points, no calculator Part 2 – 20 points, calculator permitted Prerequisite Material Finding sin, cos, tan, csc, sec, and cot of angles in both ___________ AND ____________ 5.4 Applying Trigonometric Functions Solving right triangles given _____ and _____________ _______ and solve right triangles for real world applications 5.5 Solving Right Triangles Solving equations using ___________, __________, and ____________ in degrees AND radians Evaluating expressions with a mix of trig functions and ____________ trig functions Solving right triangles given ONLY _________________ APC1: 5.4-5.5 Review Page 1 of 5 Practice I. Trig values on the Unit Circle 1. sin(225o) = ______ 2. cos(30o) = ______ 3. tan(300o) = ______ 4. csc(240o) = ______ 5. sec(180o) = ______ 6. cot(270o) = ______ 𝜋 7. tan( ) = ______ 2 8. cos( 10. sin( II. 𝜋 2 ) = ______ 4𝜋 3 ) = ______ 3𝜋 11. cot( ) = ______ 2 9. sec( 5𝜋 4 12. csc( ) = ______ 7𝜋 4 ) = ______ Solve using inverse trigonometry – write your answers in DEGREES 0 ≤ x < 360o 13. sin(x) = −√3 2 16. cot(x) = √3 APC1: 5.4-5.5 Review √2 2 14. tan(x) = −√3 15. cos(x) = 17. sec(x) = –2 18. csc(x) = −√2 Page 2 of 5 III. Solve using inverse trigonometry – write your answers in RADIANS 0 ≤ x < 2 𝝅 19. cos(x) = −√3 2 20. cot(x) = –1 21. sec(x) = 2 22. csc(x) = 2√3 3 23. tan(x) = undefined 24. sin(x) = –1 IV. Evaluate each expression. Assume that all angles are in Quadrant I. 3 25. sin(arcsin( )) 4 V. 1 26. sec(cos-1( )) 2 27. cot(tan-1(1)) Solving for missing pieces of Triangle ABC 28. If A = 38o and b = 15, find a. 29. If c = 19 and B = 87o, find a. APC1: 5.4-5.5 Review Page 3 of 5 30. If a = 16.5 and B = 65.4o, find c. 31. If a = 38 and b = 25, find A. 32. If c = 19 and b = 17, solve the whole triangle. 33. If A = 43o and c = 102, solve the whole triangle. APC1: 5.4-5.5 Review Page 4 of 5 VI. Right triangle application problems – draw and solve a triangle to fit the scenario 34. The height of a radio transmission tower is 70 meters, and it casts a shadow of length 30 meters. Find the angle of elevation of the sun. 35. An observer 2.5 miles from the launch pad of a space shuttle measures the angle of elevation to the base of the shuttle to be 25o soon after lift-off. How high is the shuttle at that instant? 36. The angle of elevation of the summit of a mountain from the bottom of a ski lift is 33o. A skier rides 1000 feet on this ski lift to get to the summit. Find the vertical distance between the bottom of the ski lift and the summit. 37. Your cat is trapped on a tree branch 6.5 meters above the ground. Your ladder is only 6.7 meters long. If you place the ladder’s tip on the branch, what angle will the ladder make with the ground? APC1: 5.4-5.5 Review Page 5 of 5