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Trig 1 notes Trig 1 notes Document Transcript

  • Trig 1 May 09, 2011 Trigonometric Ratios Objectives: 1.  To find trigonometric ratios using right triangles. 2.  Solve problems using trigonometric ratios. What is trigonometry? Trigonometry is the study of the relationships between the sides & the angles of Δ. The key to basic trigonometry to is determine which sides are involved when  looking from the angle of perspective. Angle of Perspective: the angle from which you are looking hypotenuse hypotenuse opposite adjacent side side adjacent opposite side side There are 3 basic trigonometric functions:      sine (sin) cosine (cos) tangent (tan) These trigonometric ratios are related to angle measurements.HW wkst 7­4 odds, 7­5 evens 1
  • Trig 1 May 09, 2011 Trig Ratios: (where α represents the measure  of the perspective angle) opposite side adjacent side opposite side sin α = cos α = tan α = hypotenuse hypotenuse adjacent side Find each trigonometric ratio accurate to 4 decimal places: sin 28o cos 65o tan 50o Solve for x.  Round to the nearest hundredth. x sin 50o = x tan 33o = 20 26 20 38 cos 82o = tan 17o = x xHW wkst 7­4 odds, 7­5 evens 2
  • Trig 1 May 09, 2011 Find the measure of each angle to the nearest degree. sin α =.471 cos δ = 1 tan θ = 1.57   Find the measure of the missing information accurate to the nearest whole unit. 22 x 25o y 18.6 37o n mHW wkst 7­4 odds, 7­5 evens 3
  • Trig 1 May 09, 2011 9 y o x 4 x o y 17 26HW wkst 7­4 odds, 7­5 evens 4
  • Trig 1 May 09, 2011 Angles of Elevation An angle of elevation is the angle between the line of  sight and the horizontal when an observer looks upward. Angles of Depression An angle of depression is the angle between the line of sight when an  observer looks downward, and the horizontal.HW wkst 7­4 odds, 7­5 evens 5
  • Trig 1 May 09, 2011 An airplane is flying at a height of 2 miles above the ground. The  distance along the ground from the airplane to the airport is 5 miles.  What is the angle of depression from the airplane to the airport? A building is 50 feet high. At a distance away from the building, an observer  notices that the angle of elevation to the top of the building is 41º. How far is the  observer from the base of the building?HW wkst 7­4 odds, 7­5 evens 6
  • Trig 1 May 09, 2011 HW 7­4 Wkst odds 7­5 Wkst evensHW wkst 7­4 odds, 7­5 evens 7