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Hon Math III: Unit 7 Test Circles Review Find the equation of a circle in standard form and identify the center and radius of the circle based on the given information. 1. The circle that is tangent to the y-axis and center is (-5, 4). 2. The circle that is tangent to the x-axis and center is (3,-2). 3. Center is (-3, 1) and goes through (2, 4). 4. The endpoints of a diameter are at (-2, -7) and (6, -1). 5. x2 + y2 – 6x + 10y – 8 = 0 6. x2 + y2 + 8y + 12 = 0 7. x2 + y2 + 2y – 2 = 3x + y 8. x2 + 5x + y2 = 4y + 4 Geometry of Circles Review Hon Math III: Unit 7 Test Trigonometry Review 1 – 2: Find a positive and negative coterminal angle for the given angle. (Full Rotation: 360 or 2 ) 5 1. 2. - 462o 12 3 – 4: Identify the quadrant and Convert from degrees to exact radians (answers with π). 3. -210o 4. 390o 5 – 6: Identify the quadrant and Convert from radians to degrees. 7 3 5. 6. 8 6 TRIG RATIOS (Triangle or Unit Circle): Opp or y CAH : cos Hyp Hyp 1 1 csc sec or Opp sin y SOH : sin Adj or x Hyp TOA: tan Hyp 1 1 or Adj cos x cot Opp y or Adj x Adj 1 x or Opp tan y 7 – 14: Find the exact value of the following (without a calculator – UNIT CIRCLE ). Be able to Label a blank Unit Circle with ALL ANGLES (Radian + Degree) and COORDINATES 3 11 o o 7. sin( 210 ) 8. tan 9. sec 300 10. cos 6 4 o 11. csc(450 ) 12. cot 17 6 13. sin 3 2 15 – 17: Find the value of the other 5 trig. functions. 4 8 15. cos ; lies in IV. 16. sin and tan 0 5 17 o 14. cos 240 17. tan 12 and sec 0 5 18 – 20: Complete the following triangles for the all missing sides and angles (Round to two decimals) e D F Z A 7 16 40º d y c 6 32 º E X B a C 9 Y 21 – 24: Word Problems 21. From a 90-foot lighthouse on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 4.5 . How far is the boat from the shoreline? 22. Jeremiah is looking at the top of steeple that is 120 feet from where he is standing. The angle of elevation from his eye is 67º, how tall is the steeple)? 23. A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty, which is about 305 feet tall. If the angle of elevation to the top of the statue is 200, how far is the ship from the base of the statue? 24. A 60-meter line is used to hold a hot air balloon from floating away. From the basket of the hot air balloon, the breeze from the wind creates an angle of depression of 35o. What is the ground distance of the hot air balloon to where it is held to the ground and what is the vertical distance the hot air balloon is in the air? 25 – 29: Graphing Trigonometric Functions – Be able to provide the 5 essential points in your sketch 25. f ( x ) 2 sin x 3 26. y 5 cos(4 x ) 27. g( x ) cos( x ) 2 3 28. y 3 sin( 6 x ) 4 29. y 2 cos(5 x ) 7