PreCalculus: Lesson Plan * 8/21/2006

• Quickstart p.300 - 301 #3, 7, 15, 25, 33, 39, 51, 59
  
• Unit Circle Quiz
• Lesson
  (4.3) Right Angle Trigonometry
  
  1. Definition of six trig functions (p.303)SOH CAH TOA
     sin θ = opp / hyp
     cos θ = adj / hyp
     tan θ = opp / adj
     csc θ = hyp / opp
     sec θ = hyp / adj
     cot θ = adj / opp
  2. Unit Circle coordinates
     Where did the coordinates on the Unit Circle come from?
     • Let's start with 45 ° = π/4
       If we draw a right isosceles triangle, as above, and make one of the legs have a measurement of 1, then the other leg will also equal 1 because in an isosceles triangles the legs are congruent. Using the Pythagorean theorem we determine that the hypotenuse will equal √2. Then, using the definitions of the trig functions for right triangles, we find that when θ = 45°
       sin θ = opp / hyp = 1/√2 = √2/2
       cos θ = adj / hyp = 1/√2 = √2/2
       tan θ = opp / adj = 1/1 = 1
       The other three functions can be determined in a like manner.
       
     
     
     • Now let's investigate for 30° = π/6 and 60° = π/3
       In an equilateral triangle, each angle measures 60° (180°/3).
       Drawing a perpendicular bisector creates two triangles with angle measures 30°-60°-90°.
       
       If each side of the equilateral triangle measures 2, then the hypotenuse of our right triangle will measure 2 and the shortest leg (opposite the 30°angle) will measure 1 (half of 2). Using the Pythagorean Theorem, the length of the other leg (opposite the 60° angle) will equal √3.
       
       Then, using the definitions of the trig functions for right triangles, we find that
       when θ = 30° = π/6
       sin θ = opp / hyp = 1/2
       cos θ = adj / hyp = √3/2
       tan θ = opp / adj = 1/√3= √3/3
       The other three functions can be determined in a like manner.
       
       when θ = 60° = π/3
       sin θ = opp / hyp = √3/2
       cos θ = adj / hyp = 1/2
       tan θ = opp / adj = √3/1= √3
       The other three functions can be determined in a like manner.
     3. Trig Identities
     
     • Pythagorean Identities
     • Quotient Identities
     • Reciprocal Identities
       
• HW p.310 - 313: 3 - 18 x 3's