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TRIGONOMETRY FINAL EXAM REVIEW CHAPTERS 1 – 4 Name:_________________________________________ Define the following: 1. Domain: 2. Range: 3. Function: 4. Vertical Line Test: 5. Standard Position 6. Quadrantal 7. Coterminal 8. Negative angle 9. Positive angle Define the following in terms of x, y, and r: 10. Sine: 11. Cotangent: 12. Cosine: 13. Secant: 14. Tangent: 15. Cosecant: 1 Convert the degrees to radians and the radians to degrees. The conversion factor for degrees to radians is: The conversion factor for radians to degrees is: 16. 132 degrees to radians 17. 245 degrees to radians 18. 2π/3 to degrees 19. 11π/6 to degrees Answer the following: 20. What angle measurements (in degrees and radians) are in each quadrant? I: II: III: IV: 2 21. Find the reference angle for (draw a sketch) a. 215 degrees b. 345 degrees c. – 120 degrees 22. Find the distance between P(3, -2) and Q (5, 2). The distance formula is: 23. The terminal side of an angle passes through the point (3, 4). Find the cosine of the angle. Draw a sketch. 24. The terminal side of angle passes through the point (5, 3). Find the sine of the angle. Draw a sketch 3 25. The measure of an angle in standard position lies in Q III. The Tan of the angle is ½. Find the sin of the angle. Draw a sketch 26. What are the ratios of the “special” triangles? a. 30:60:90 b. 45:45:90 27.) State whether the following functions are + or – in the quadrants: Function QI QII QIII QIV Sin Cos Tan Sec Csc Cot 28.) The angle of depression from an airplane to the base of a monument is 60 degrees. The altitude of the airplane is 100 meters. Determine the line of sight distance from the plane to the base of the monument. Draw a sketch. Give your answer to the nearest tenth of a meter. 4 29.) In a right triangle A= 40, and c = 12. Find side b 30.) In a right triangle a = 15 and b = 12. Find angle B 31.) For the graph of y = 2 sin 3x + 4, find the following and then graph. c. amplitude d. vertical shift e. phase shift f. period g. Graph from - 2π to 2π 32.) For the graph of y = 2 cos (x + π) find the following and then graph. h. amplitude i. vertical shift j. phase shift k. period 5 l. Graph from - 2π to 2π 33.) A wheel rotates at 75 rpm. Find the angular velocity of the wheel. 34.) A wheel spinning at an angular velocity of 200 rad/sec. Find the distance traveled by a point 8 cm from the center during 2 sec. 35.) Use sin (a + b) to find the exact value of sin 75 (no decimals) 36.) Use cos (a – b) to find the exact value of cos 15 (no decimals) 37.) In a triangle: A = 80 B = 75 and c = 40. Find the missing sides and angles. 6 38.) In a triangle A = 65 b = 5 and c = 8. Find the missing sides and angles. 39.) Find the number of solutions to the following triangles: B = 120 a = 15 b = 17 A = 43 a=8 b = 10 A = 95 a = 12 b = 10 40.) Find the area of the triangle if a = 2, b = 4, c =5 41.) Find the area of a triangle if a = 15, b = 18 and C = 58 degrees 7 42.) Prove: 43.) Prove : 44.) 1 + tan 2 Ө = sec 2 Ө tan Ө 1 - cos 2 Ө = sec Ө csc Ө Prove: csc2 θ ( 1 - cos2 θ) = 1 45.) Prove: cot2 θ = csc2 θ – 1 8