Trigonometry 2 Questions and Answers - Form 3 Topical Mathematics

Questions

1. If tan x^º = 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 0^º ≤ θ ≤ 360^º
3. Without a mathematical table or a calculator, simplify:
   
   giving your answer in rationalized surd form.
4. Express in surds form and rationalize the denominator.
   
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
   
7. John cycles from shopping centre A on a bearing of 120^º for 5 km to shopping centre B. He then cycles on a bearing of 200^º 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. 
   
   5 sin x + cos x
   = 5 (¹²/₁₃) − ⁵/₁₃
   = ⁶⁰/₁₃ − ⁵/₁₃ = ⁵⁵/₁₃
   = ¹²/₁₃ 
   
   
   
   
2.  
   
3.  
   
4.  
   
5.  
   
6.  
   
7. 1. b^² = a^² + c^² – 2ac cos B
      b^² = 7^² + 5^² – 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 ≃ 32^º
      32 – 20 = 12^º
      Bearing = 360^º - 12^º = 348^º
   3. 020^º