PreCalculus: Lesson Plan * 8/22/2006

• Quickstart p.313 #81 - 88
• Lesson
  (4.3) Right Angle Trigonometry (cont.)
  
  1. Proving Trig Identities
     
  2. Using Trig Identities
     Example: If θ is an acute angle such that cosθ = 0.3, then find the following
     a) sinθ
     Solution: Use the Pythagorean Identity (sinθ)^2 + (cosθ)^2 = 1
     (sinθ)^2 + (0.3)^2 = 1
     (sinθ)^2 = 1 - (3/10)^2
     (sinθ)^2 = 1 - (9/100)
     (sinθ)^2 = 91/100
     sinθ = √91/10
     b) tanθ
     Solution: Use the quotient identity tanθ = sinθ/cosθ
     c) cotθ
     Solution: Use the reciprocal identity cotθ = 1/tanθ
     d) secθ
     Solution: Use the reciprocal identity secθ = 1/cosθ
     e) cscθ
     Solution: Use the reciprocal identity cscθ = 1/sinθ
     
  3. Applications with Right Triangles
     Example: If the sun is 30° up from the horizon and shining on a tree forming a 50 foot shadow, how tall is the tree?
     Solution: Draw a picture
     h/50 = tan30°
     h = 50 tan30°
     h = 50(√3/3) ≈ 28.82 feet
     
  4. Evaluating Trig Functions with a calculator
     Make sure your calculator is in the correct mode, radians or degrees, when calculating trig values
     
• HW p.310 - 313 21 - 63 x 3's