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Name ______________________________________________ Date________ Trigonometry – Cumulative Review #1 Chapter 9 : Trig Basics What you need to know!! Special Right Triangles: Use to find exact trig values of 30 , 45 , 60 . The Unit Circle: use to find trig functions of quadrantal (multiple of 90 ) angles All Student Take Calculus: Tells you which trig function is positive in which quadrant. Please note: a trig function’s RECIPROCAL function has the same sign (+/-) SOHCAHTOA The buttons sin-1, cos-1, and tan-1 will give you the angle when you know the value of the trig function. There are no buttons for sec -1, csc-1, and cot-1. 1. Find Ans: 4/3 3. Find Ans: Sec is the reciprocal of cos Csc is the reciprocal of sin Cot is the reciprocal of tan 2. Find Ans: 5/4 4. Find cos A if b=16, a=12, c=20 where is the right angle. Ans: 4/5 C Name ______________________________________________ Date________ 5. Use the appropriate trigonometric ratio to find the value of x. Ans: 10.5 7. Use the appropriate trigonometric ratio to find the value of 6. Use the appropriate trigonometric ratio to find the value of . Ans: 68 8. The angle of elevation to the top of the empire state building from a distance 1 mile away is 11 . Find the height of the building to the nearest foot. Ans: .19 miles Ans: 46 9. In what quadrant is 160 ? Ans: II 11. Find a positive coterminal angle for 100 Ans: 260 13. Find 10. In what quadrant is -130 ? Ans: III 12. In what quadrant is angle tan ? and Ans: III 14. The point (9, -40) is a point on the terminal ray of an angle in standard form on the coordinate plane. Find the sin of the angle. Ans: -40/41 Ans: -2/3 if sin Name ______________________________________________ Date________ 15. If sin tan . where is in quadrant II, find Ans: 17. What is the reference angle for 200 ? 16. Find the exact value of 2cos30 + 4 tan 60 Ans: 18. Find the exact value of sin 210 Ans: -1/2 Ans: 20 19. Find the exact value of csc 120 20. Find the exact value of cot 315 Ans: : Ans: -1 Name ______________________________________________ Date________ Trigonometry – Cumulative Review #2 Chapter 10: Radians What you need to know!! Relationship between a central angle and an arc: where S=length of arc, is the measure of the central angle in radians, and the radius of the circle. is Cofunctions have angles that are complementary (add to 90 ). Sine and Cosine, Tangent and Cotangent, and Secant and Cosecant are cofunctions. Example: sin 20 = cosine 70 . 1. The radius of a circle is 10”. Find the length of an arc intercepted by a central angle of 2 radians. To convert from degrees to radians: multiply by To convert from radians to degrees: multiply by You also need all of the information from the Chapter 9 Cumulative Review Handout! 2. Convert 40 to radians. Ans: : Ans: : 3. Convert 4. Find the exact value of sin . to degrees. Ans: : Ans: : 5. Find the exact value of cos . 6. Find the exact value of tan . Ans: : Ans: : 7. Find the exact value of sin Ans: : . 8. Find the exact value of tan Ans: : . Name ______________________________________________ Date________ 9. If , find . Ans: : 10. Find the exact value of csc . Ans: : 11. If sin 3x=cos 7x, find the value of x. 12. If tan (x+20) =cot (3x- 40 ), find the value of x. Ans: : Ans: : Name ______________________________________________ Date________ Trigonometry – Cumulative Review #2 QUIZ Chapter 9/10 1. Draw the unit circle here, and label the 2. Draw the special right triangles here, coordinates at the quadrantal (multiple of labeling the angles AND the sides. 90 ) angles. 3. Convert to radians. 5. Find the exact value of tan ALL WORK. 4. Convert , showing 7. If sec (x+10 )=csc (3x-20), find the value of x. Show your work. to degrees. 6. Find the exact value of sec showing ALL WORK. 8. What is the reference angle for 250 ? , Name ______________________________________________ Date________ Trigonometry – Cumulative Review #3 “Cheating” with your calculator for MULTIPLE CHOICE problems. Press MODE, and make sure it is set to DEGREES mode. In order to do this, you MUST memorize these decimal approximations: (I’m hoping you already know that ½ = .5 exactly.) Using a calculator to help you, find the exact value of 1. Sin 30 2. Cos 30 3. Tan 30 4. Sin 60 5. Cos 60 6. Tan 60 7. Sin 45 8. Cos 45 9. Tan 45 Using a calculator is great because they you don’t have to do all that reference angle and ATSC stuff to find the exact value of angles greater than 90 . Just type it in the calculator!! 10. Sin 150 11. Cos 150 12. Tan 150 13. Sin 315 14. Cos 315 15. Tan 315 16. Sin 240 17. Cos 240 18. Tan 240 You can also find the exact values in this manner if the problem is given in radians. Just make sure you press MODE, and make sure it is set to RADIANS mode. 19. Sin 20. Cos 21. Tan 22. Sin 23. Cos 24. Tan Name ______________________________________________ Date________ Your calculator can find the exact trig value of any quadrantal angle. Use the appropriate mode of your calculator to find the exact value of: 25. Sin 0 26. Cos 90 27. Tan 180 28. Sin 29. Cos 30. Tan You can use these values to help you find the exact reciprocal trig functions as well. 31. cot 0 32. csc 90 33. sec 180 34. csc 270 35. sec 360 36. cot 90 37. cot 30 38. csc 60 39. sec 45 40. csc 150 41. sec 135 42. cot 300 Name ______________________________________________ Date________ Trigonometry Homework: USE YOUR CALCULATOR to get the exact value of the following. Make sure your MODE is set to radians or degree when it is necessary. 1. Sec 0 2. Cos 90 3. csc 45 4. tan 60 5. cot 30 6. tan 135 7. sin 330 8. Cos 315 9. Sec 210 10. Cos 240 11. Sec 12. Cos 13. csc 14. tan 15. sec 16. cos Name ______________________________________________ Date________ Trigonometry – Cumulative Review #4 Chapter 9, 10 using the calculator to help!!. 1. Find Ans: 5/4 3. Find Ans: 5. Use the appropriate trigonometric ratio to find the value of x to the nearest tenth. Ans: 10.5 7. In what quadrant is 300 ? Ans: IV 9. Find a positive coterminal angle for -30 Ans: 330 2. Find Ans: 3/4 4. Find cot A if b=16, a=12, c=20 where C is the right angle. Ans: 4/3 6. Use the appropriate trigonometric ratio to find the value of to the nearest degree. Ans: 68 8. In what quadrant is -100 ? Ans: III 10. In what quadrant is angle and cos ? Ans: IV if sin Name ______________________________________________ Date________ 11. Find sin 12. The point (9, -40) is a point on the terminal ray of an angle in standard form on the coordinate plane. Find the cos of the angle. Ans: 9/41 Ans: 13. If sin where find cos . 14. Find the exact value of 2cos30 + 4 tan 60 is in quadrant II, (recall you can use your calculator to help you get the exact values if you remember the decimal approximations) Ans: Ans: 15. What is the reference angle for 250 ? 16. Find the exact value of sin 240 Ans: Ans:70 17. Find the exact value of sec 120 Ans: -2 19. Find the exact value of sin 90 Ans:1 21. Convert 50 to radians Ans: 18. Find the exact value of sin 315 Ans: 20. Find the exact value of tan 270 Ans: undefined 22. Convert Ans:120 to degrees Name ______________________________________________ Date________ 23. Determine the exact value of tan . Ans: 24. Determine the exact value of sin . Ans: 25. Determine the exact value of sec Ans: undefined 27. If Ans: 70 . 26. Determine the exact value of csc . Ans: , find x. 28. If Ans: , find x. Name ______________________________________________ Date________ What you need to know!! Chapter 9 and 10 Special Right Triangles: Use to find exact trig values of 30 , 45 , 60 . The Unit Circle: use to find trig functions of quadrantal (multiple of 90 ) angles All Student Take Calculus: Tells you which trig function is positive in which quadrant. Please note: a trig function’s RECIPROCAL function has the same sign (+/-) The buttons sin-1, cos-1, and tan-1 will give you the angle when you know the value of the trig function. There are no buttons for sec -1, csc-1, and cot-1. SOHCAHTOA Sec is the reciprocal of cos Csc is the reciprocal of sin Cot is the reciprocal of tan Relationship between a central angle and an arc: where S=length of arc, is the measure of the central angle in radians, and is the radius of the circle. To convert from degrees to radians: multiply by Cofunctions have angles that are complementary (add to 90 ). Sine and Cosine, Tangent and Cotangent, and Secant and Cosecant are cofunctions. Example: sin 20 = cosine 70 . You also need all of the information from the Chapter 9 Cumulative Review Handout! To convert from radians to degrees: multiply by (I’m hoping you already know that ½ = .5 exactly.) Name ______________________________________________ Date________ Trigonometry PRACTICE QUIZ #2 Chapter 9/10 1. Draw the unit circle here, and label the coordinates at the quadrantal (multiple of 90 ) angles. 3. Convert to radians. 2. Draw the special right triangles here, labeling the angles AND the sides. 4. Convert to degrees. Ans: Ans: 5. Find the exact value of tan 6. Find the exact value of sec Ans: Ans: 7. If sin (x+10 )=cos (3x-20), find the value of x. Show your work. 8. What is the reference angle for 100 ? Ans: Ans: Name ______________________________________________ Date________ Trigonometry QUIZ #2 1. Draw the unit circle here, and label the coordinates at the quadrantal (multiple of 90 ) angles. 3. Convert to radians. 5. Find the exact value of tan 7. Find Chapter 9/10 2. Draw the special right triangles here, labeling the angles AND the sides. 4. Convert to degrees. 6. Find the exact value of csc 8. Find cot A if b=6, a=8, c=10 where C is the right angle. Name ______________________________________________ Date________ 9. Use the appropriate trigonometric ratio to find the value of x to the nearest tenth. 10. Use the appropriate trigonometric ratio to find the value of to the nearest degree. 15 50 5 2 11. In what quadrant is 250 ? 12. In what quadrant is -200 ? 13. Find a positive coterminal angle for -50 14. In what quadrant is angle sin and tan ? if Name ______________________________________________ Date________ Trigonometry – Cumulative Review #5 Chapter 11 – Trig Graphing Standard form of a trig equation: What you need to know!! is the amplitude b is the frequency d is the midline shift is the period Period = Vocabulary amplitude: how high above the midline the graph reaches Frequency: how many complete cycles of sine or cosine you see from 0 to Period: how long it takes to make one cycle of a sine or cosine curve Midline: the horizontal center of the graph and frequency= sine cosine a is + a is - Determine the equation of each of the following. Name ______________________________________________ Date________ Equation 1. 2. 3. 4. 5. Amplitude Frequency Period midline