Unit Circle – Class Work

Find the exact value of the given expression.

  1. 2. 3.
  1. 5. 6.
  1. Given the terminal point
  2. Given the terminal point
  3. Knowing cosx=and the terminal point is in the fourth quadrant find sinx.
  4. Knowing cotx=and the terminal point is in the third quadrant find secx.

Unit Circle – Home Work

Find the exact value of the given expression.

  1. 12. 13.
  1. 15. 16.
  1. Given the terminal point
  2. Given the terminal point
  3. Knowing sinx=and the terminal point is in the second quadrant find secx.
  4. Knowing cscx=and the terminal point is in the third quadrant find cotx.

Graphing – Class Work

State the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.

  1. 22.
  1. 24.

Graphing – Home Work

State the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.

  1. 27.
  1. 29.

Law of Sines – Class Work

Solve triangle ABC.

  1. 32.
  1. 34.
  1. 36.

  2. An airplane is on the radar at both Newark Liberty International and JFK airports that are 20 miles apart. The angle of elevation from Newark to the plane is and from JFK is when the plane is directly between them. How far is the plane from JFK? What is the plane’s elevation?
  3. A mathematician walking in the woods noticed that the angle the angle of elevation to a bird at the top of a tree is , after walking 40’ toward the tree, the angle is How far is she from the bird?

Law of Sines – Home Work

Solve triangle ABC.

  1. 41.
  1. 43.
  1. 45.

  2. An airplane is on the radar at both Newark Liberty International and JFK airports that are 20 miles apart. The angle of elevation from Newark to the plane is and from JFK is when the plane is directly between them. How far is the plane from JFK? What is the plane’s elevation?
  3. A mathematician walking in the woods noticed that the angle the angle of elevation to a bird at the top of a tree is , after walking 30’ toward the tree, the angle is How far is she from the bird?

Law of Cosines – Class Work

Solve triangle ABC.

  1. 50.
  1. 52.
  1. 54.
  1. A ship at sea noticed two lighthouses that according to the charts are 1 mile apart. The light at lighthouse A is 200’ above sea level and the navigator on the ship measures the angle of elevation to be, how far is the ship from lighthouse A? The light at lighthouse B is 300’ above sea level and the navigator on the ship measures the angle of elevation to be , how far is the ship from lighthouse B? How far is the ship from shore?
  2. A student takes his 2 dogs for a walk. He lets them off their leash in a field where Edison runs at 7 m/s and Einstein runs at 6 m/s. The student determines the angle between the dogs is , how far are the dogs from each other in 8 seconds?

Law of Cosines – Home Work

Solve triangle ABC.

  1. 58.
  1. 60.
  1. 62.
  1. A ship at sea noticed two lighthouses that according to the charts are 1 mile apart. The light at lighthouse A is 275’ above sea level and the navigator on the ship measures the angle of elevation to be , how far is the ship from lighthouse A? The light at lighthouse B is 325’ above sea level and the navigator on the ship measures the angle of elevation to be , how far is the ship from lighthouse B? How far is the ship from shore?
  1. A student takes his 2 dogs for a walk. He lets them off their leash in a field where Edison runs at 10 m/s and Einstein runs at 8 m/s. The student determines the angle between the dogs is , how far are the dogs from each other in 5 seconds?

Pythagorean Identities – Class Work

Simplify the expression

  1. 66.
  1. 68.
  1. 70.
  1. 72.

Verify the Identity

  1. 75.
  1. 77.

Pythagorean Identities – Home Work

Simplify the expression

  1. 79.
  1. 81.
  1. 83.
  1. 85.

Verify the Identity

  1. 88.
  1. 90.

Angle Sum/Difference Identity – Class Work

Use Angle Sum/Difference Identity to find the exact value of the expression.

  1. 92.
  1. 94.
  1. 96.

Verify the Identity.

  1. 98.
  1. 100.

Angle Sum/Difference Identity – Home Work

Use Angle Sum/Difference Identity to find the exact value of the expression.

  1. 102.
  1. 104.
  1. 106.

Verify the Identity.

  1. 108.
  1. 110.

Double Angle Identity – Class Work

Find the exact value of the expression.







Verify the Identity.

  1. 118.

  3. 120.

Double Angle Identity – Home Work

Find the exact value of the expression.






Verify the Identity.

  1. 128.

Half Angle Identity – Class Work

Find the exact value of the expression.

  1. 131.
  1. 133.

Verify the Identity.


Half Angle Identity – Home Work

Find the exact value of the expression.

  1. 136.
  1. 138.

Verify the Identity.

Power Reducing Identity – Class Work

Simplify the expression.

  1. 141.

  2. Find if and is in the first quadrant.
  3. Find if and is in the third quadrant.

Power Reducing Identity – Home Work

Simplify the expression.

  1. 146.

  2. Find if and is in the fourth quadrant.
  3. Find if and is in the third quadrant.

Sum to Product Identity – Class Work

Find the exact value of the expression.

  1. 151. 152.

Verify the Identity.

  1. 154. 155.

Sum to Product Identity – Home Work

Find the exact value of the expression.

  1. 157. 158.

Verify the Identity.

  1. 160.

Product to Sum Identity – Class Work

Find the exact value of the expression.

  1. 163.
  1. 165.

Product to Sum Identity – Home Work

Find the exact value of the expression.

  1. 167.
  1. 169.

Inverse Trig Functions – Class Work

Evaluate the expression.

  1. 170.
  2. 172.
  1. 174.
  1. 176.
  1. 178.

Inverse Trig Functions – Home Work

Evaluate the expression.

  1. 180.
  1. 182.
  1. 184.
  1. 186.
  1. 188.

Trig Equations – Class Work

Find the value(s) of x such that , if they exist.

  1. 190.
  1. 192.
  1. 194.
  1. 196.
  1. 198.

Trig Equations – Home Work

Find the value(s) of x such that, if they exist.

  1. 201.
  1. 203.
  1. 205.
  1. 207.
  1. 209.

Trigonometry Unit Review
Multiple Choice

  1. Given the terminal point of find
  2. -1
  3. 1
  4. Knowing and the terminal point is in the second quadrant find
  5. What is the phase shift of
  6. The difference between the maximum of and is
  7. 1
  8. 2
  9. 3
  10. 8
  11. Given
  12. 18.418
  13. 53.418
  14. 91.582
  15. both a and b
  16. Given
  17. 1.021
  18. 40
  19. 128.979
  20. no solution
  21. Given
  22. 6.188
  23. 32.456
  24. 47.967
  25. 82.033
  26. Find the exact value of
  27. On the interval , , thus x =
  28. 0
  29. all of the above
  30. Find the exact value of
  31. Rewrite as a sum or difference.
  32. On the interval ,
  33. no solution on the interval given
  34. Undefined
  35. On the interval , solve

I. 0 II. III.

  1. I only
  2. II and III
  3. I and III
  4. I, II, and III

Extended Response

  1. The range of a projectile launched at initial velocity and angle is

,

where r is the horizontal distance, in feet, the projectile will travel.

  1. Rewrite the formula using double angle formula.
  2. A golf ball is hit 200 yards, if the initial velocity 200 ft/sec, what was the angle it was hit?
  3. If the golfer struck the ball at 45, how far would the ball traveled?
  1. A state park hires a surveyor to map out the park.
  2. A and B are on opposite sides of the lake, if the surveyor stands at point C and measures angle ACB= 50 and CA= 400’ and CB= 350’, how wide is the lake?
  3. At a river the surveyor picks two spots, X and Y, on the same bank of the river and a tree, C, on opposite bank. Angle X= 60 and angle Y= 50 and XY=300’, how wide is the river? (Remember distance is measured along perpendiculars.)
  4. The surveyor measured the angle to the top of a hill at the center of the park to be 32. She moved 200’ closer and the angle to the top of the hill was 43 How tall was the hill?
  5. The average daily production, M (in hundreds of gallons), on a dairy farm is modeled by

where d is the day, d=1 is January first.

  1. What is the period of the function?
  2. What is the average daily production for the year?
  3. Using the graph of M(d), what months during the year is production over 5500 gallons a day?
  1. A student was asked to solve the following equation over the interval . During his calculations he might have made an error. Identify the error and correct his work so that he gets the right answer.

Pre-Calc Trig~1~NJCTL.org