Trigonometry 2 Questions and Answers - Form 3 Topical Mathematics

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Questions

  1. If tan xº = 12/5 and x is a reflex angle, find the value of 5sinx + cos x without using a calculator or mathematical tables
  2. Find θ given that 2 cos 3θ -1 = 0 for 0º ≤ θ ≤ 360º
  3. Without a mathematical table or a calculator, simplify:
    Trig 2 Q3
    giving your answer in rationalized surd form.
  4. Express in surds form and rationalize the denominator.
    Trig 2 Q4
  5. Simplify the following without using tables;
    Tan 45 + cos 45sin 60
  6. Simplify the following surds in the form of a + √b c where a, b, and c are constants
    Trig 2 Q6
  7. John cycles from shopping centre A on a bearing of 120º for 5 km to shopping centre B. He then cycles on a bearing of 200º for 7 km to the shopping centre C. Calculate to 1 decimal place.
    1. The direct distance from A to C.
    2. The bearing of A from C.
    3. Bearing of B from C.

Answers


  1. Trig A1
    5 sin x + cos x
    = 5 (12/13) − 5/13
    = 60/135/13 = 55/13
    = 12/13 



  2.  
    Tri AA2
  3.  
    Trig A3
  4.  
    Trig 6 fin
  5.  
    Trig A5
  6.  
    Trig A7
    1. b² = a² + c² – 2ac cos B
      b² = 7² + 5² – 2.5.. 7 cos 100
      = 74 – 70(-0.173648)
      = 74 + 12.15537
      b² = 86.15537
      b = 9.28199
      AC = 9.3 km
    2. 9.3/sin100 = 5/sinθ
      Sin θ = 5sin100/9.3 = 0.529466
      θ = 31.9694
      θ ≃ 32º
      32 – 20 = 12º
      Bearing = 360º - 12º = 348º
    3. 020º 

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