Name: ______Date:______Class:_____

TRIG 450 1st Semester Final Study Guide 2016-17!!!

Unit 1.1: Trigonometry Foundations

  1. Convert 650° 24’ 18” to decimal degree notation. Round your answer to the nearest thousandths place.
  1. Convert 74.555° to degrees/minutes/seconds. Round your answer to the nearest second.
  1. Convert 517.678° to D/M/S. Round your answer to the nearest second.
  1. Convert 51.357° degrees to D/M/S. Round your answer to the nearest second.
  1. Convert 93°10' 43" to decimal equivalent. Round your answer to the nearest thousandths place.
  1. Convert -61.57° to D/M/S equivalent. Round your answer to nearest second.
  1. Convert 381.77° to D/M/S equivalent. Round your answer to nearest second.
  1. Convert 23°23' 23" to decimal equivalent. Round your answer to nearest thousandths place.
  1. Explain the difference between a positive angle measure and a negative angle measure.
  1. Write an expression for the measures of all angles that are coterminal with 520°. Then, use your expression to find one positive angle and one negative angle that are coterminal with 520°.
  1. Give the angle measure represented by each rotation:
  2. 2.5 rotations clockwise
  1. 6.3 rotations counterclockwise
  1. Find the measure of the reference angle for each angle:
  2. 113°
  1. 481°
  1. 327°
  1. -420°
  1. -79°

f. 1500°

  1. Is -540° a quadrantal angle? Please explain why or why not.

Unit 1.2: Using the Unit Circle

Use the unit circle and your ratio table to find the given values. Simplify the radical when appropriate.

  1. Sin (30°)
  1. Cos (45°)
  1. Tan (60°)
  1. Csc (90°)
  1. Sec (120°)
  1. Cot (135°)
  1. Sin (150°)
  1. Cos (180°)
  1. Tan (210°)
  1. Csc (225°)
  1. Sec (240°)
  1. Cot (270°)
  1. Sin (300°)
  1. Cos (315°)
  1. Tan (330°)
  1. Csc (360°)
  1. Sec (675°)
  1. Cot (570°)

Unit 2.1: Trigonometry with Right Triangles

  1. Find the sine, cosine and tangent ratios of .


  1. Find the value of each variable.
  1. Find the value of a

  1. Find the value of x.

  1. Find the value of each variable:

  1. A building casts a shadow that is 210 feet long and makes an angle of 40 with the top of the building. Find the height of the building.


  1. You are flying a kite with a 100-foot long string at an angle of elevation of 52. Approximately how high is the kite above the ground?

  1. Find the measures of A and C.

  1. Find the measures of A and C.
  1. If what is
  1. What is the value of ?
  1. An 80-foot ladder is propped up to the wall of the building. The latter reaches a window sill that is 60 feet above the ground. What angle does the latter make with the ground?
/
  1. Find the sine, cosine and tangent ratios of .




  1. Find the value of each variable.
  1. Find the value of a


  1. Find the value of x.

  1. Find the value of each variable:


  1. A building casts a shadow that is ______feet long and makes an angle of ______ with the top of the building. Find the height of the building.



  1. You are flying a kite with a 100-foot long string at an angle of elevation of ______. Approximately how high is the kite above the ground?


  1. Find the measures of A and C.



  1. Find the measures of A and C.
  1. If what is
  1. What is the value of ?
  1. An ______-foot ladder is propped up to the wall of the building. The latter reaches a window sill that is ______feet above the ground. What angle does the latter make with the ground?


Unit 2.2: Law of Sines for Non-Right Triangles

  1. Find the value of .
/
  1. Find the value of .

  1. Find the mC.
/
  1. Find the mC.

  1. Find the area of the triangle.
/
  1. Find the area of the triangle.

A surveyor needs to determine the distance between two points and that lie on opposite banks of a river. A point is chosen meters from point , on the same side of the river as . The measures of angles and are and , respectively. Approximate the distance from to to the nearest meter.

In , , , and . Find . Include a diagram in your answer.

Unit 3.1: Converting Radians Degrees

Convert degrees to radians and radians to degrees.

1. 150o2. 210o3. -60o4. 180o

5. -240o6. 540o 7. 28.

9. 10. 11. 12.

Unit 3.2: Using proportions to find Arc Length and Sector Area

1.Find circumference. / 2.Find sector area.
3.Find . / 4.Find area of circle.
5.Find area of circle. / 6.Find arc length.
7.Find . / 8.Find radius.
9.Find area of circle. / 10.Find sector area.
11.Find . / 12.Find circumference.
13.Find circumference. / 14.Find arc length.
15.Find . / 16.Find radius.