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Worksheet: Solving Equations Involving a Half-Angle

Q1:

Solve t a n s i n ο€» π‘₯ 2  = π‘₯ , where 0 ≀ π‘₯ < 2 πœ‹ .

  • A π‘₯ ∈  0 , πœ‹ 2 
  • B π‘₯ ∈  0 , πœ‹ 2 , 3 πœ‹ 2 , 2 πœ‹ 
  • C π‘₯ ∈  0 , πœ‹ 4 , πœ‹ , 3 πœ‹ 4 
  • D π‘₯ ∈  0 , πœ‹ 2 , 3 πœ‹ 2 
  • E π‘₯ ∈  0 , πœ‹ 4 

Q2:

By using the half angle formula s i n c o s ο€» π‘₯ 2  = ο„ž 1 βˆ’ π‘₯ 2 , or otherwise, solve the equation s i n c o s ο€» π‘₯ 2  + π‘₯ = 1 , where 0 ≀ π‘₯ < 2 πœ‹ .

  • A π‘₯ =  0 , 1 6 πœ‹ 
  • B π‘₯ =  0 , 1 3 πœ‹ 
  • C π‘₯ =  0 , 1 6 πœ‹ , 5 6 πœ‹ 
  • D π‘₯ =  0 , 1 3 πœ‹ , 5 3 πœ‹ 
  • E π‘₯ =  0 , 1 3 πœ‹ , 5 6 πœ‹ 