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Worksheet: Simple Trigonometric Equations

Q1:

Find the set of values satisfying √ 2 πœƒ πœƒ βˆ’ πœƒ = 0 s i n c o s c o s where 0 ≀ πœƒ < 3 6 0 ∘ ∘ .

  • A { 4 5 , 1 3 5 , 1 8 0 } ∘ ∘ ∘
  • B { 4 5 , 9 0 , 3 1 5 } ∘ ∘ ∘
  • C { 1 8 0 , 2 2 5 , 3 1 5 } ∘ ∘ ∘
  • D { 4 5 , 9 0 , 1 3 5 } ∘ ∘ ∘

Q2:

Find the set of values satisfying 2 πœƒ πœƒ βˆ’ πœƒ = 0 s i n c o s c o s where 0 ≀ πœƒ < 3 6 0 ∘ ∘ .

  • A { 3 0 , 9 0 , 1 2 0 } ∘ ∘ ∘
  • B { 6 0 , 9 0 , 1 2 0 } ∘ ∘ ∘
  • C { 6 0 , 1 8 0 , 1 5 0 } ∘ ∘ ∘
  • D { 3 0 , 9 0 , 1 5 0 } ∘ ∘ ∘

Q3:

Find the solution set of t a n t a n t a n t a n π‘₯ + 7 + π‘₯ 7 = 1 ∘ ∘ , where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 3 8 , 2 3 2 } ∘ ∘
  • B { 5 2 , 2 3 2 } ∘ ∘
  • C { 5 2 , 2 1 8 } ∘ ∘
  • D { 3 8 , 2 1 8 } ∘ ∘

Q4:

Find the solution set of s i n c o s c o s s i n π‘₯ 1 6 βˆ’ π‘₯ 1 6 = √ 2 2 ∘ ∘ , where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 2 9 ∘ , 1 5 1 } ∘
  • B { 2 9 ∘ , 1 1 9 } ∘
  • C { 6 1 ∘ , 1 1 9 } ∘
  • D { 6 1 ∘ , 1 5 1 } ∘

Q5:

Find the solution set for π‘₯ given c o s c o s s i n s i n π‘₯ 2 π‘₯ βˆ’ π‘₯ 2 π‘₯ = 1 2 where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 1 0 , 1 0 0 } ∘ ∘
  • B { 1 0 , 1 1 0 } ∘ ∘
  • C { 2 0 , 1 1 0 } ∘ ∘
  • D { 2 0 , 1 0 0 } ∘ ∘

Q6:

Find the solution set for π‘₯ given s i n c o s c o s s i n π‘₯ 3 5 + π‘₯ 3 5 = √ 2 2 ∘ ∘ where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 1 0 ∘ , 1 7 0 } ∘
  • B { 8 0 ∘ , 1 7 0 } ∘
  • C { 8 0 ∘ , 1 0 0 } ∘
  • D { 1 0 ∘ , 1 0 0 } ∘

Q7:

Find the solution set of π‘₯ given t a n t a n t a n t a n π‘₯ βˆ’ 6 4 1 + π‘₯ 6 4 = 1 ∘ ∘ where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 1 0 9 , 1 6 1 } ∘ ∘
  • B { βˆ’ 1 9 , 2 8 9 } ∘ ∘
  • C { βˆ’ 1 9 , 1 6 1 } ∘ ∘
  • D { 1 0 9 , 2 8 9 } ∘ ∘

Q8:

Find the solution set of πœƒ given t a n t a n t a n t a n 2 5 πœƒ βˆ’ 2 3 πœƒ 1 + 2 5 πœƒ 2 3 πœƒ = √ 3 where 0 < πœƒ < 9 0 ∘ ∘ .

  • A { 6 0 } ∘
  • B { 4 5 } ∘
  • C { 1 5 } ∘
  • D { 3 0 } ∘

Q9:

Find the solution set of the equation s i n s i n s i n s i n ( 6 7 + 2 πœƒ ) ( 7 9 + πœƒ ) + ( 2 3 βˆ’ 2 πœƒ ) ( 1 1 βˆ’ πœƒ ) = 1 ∘ ∘ ∘ ∘ given 0 < πœƒ < πœ‹ 2 .

  • A { 3 4 } ∘
  • B { 1 4 6 } ∘
  • C { 9 0 } ∘
  • D { 1 2 } ∘

Q10:

Find the set of possible values of π‘₯ which satisfy 1 √ π‘₯ βˆ’ π‘₯ = 2 c o s c o s 2 4 where 0 < π‘₯ < 3 6 0 ∘ ∘ .

  • A { 4 5 , 1 3 5 , 2 1 0 , 3 3 0 } ∘ ∘ ∘ ∘
  • B { 4 5 , 1 5 0 , 2 4 0 , 3 0 0 } ∘ ∘ ∘ ∘
  • C { 4 5 , 1 3 5 } ∘ ∘
  • D { 4 5 , 1 3 5 , 2 2 5 , 3 1 5 } ∘ ∘ ∘ ∘

Q11:

Find π‘š ∠ πœƒ given c o s s i n s i n c o s 3 4 . 5 3 4 . 5 + 1 2 6 9 = πœƒ ∘ ∘ ∘ where πœƒ is a positive acute angle.

Q12:

Find the set of solutions in the range 0 < π‘₯ < 1 8 0 for the equation ( π‘₯ + π‘₯ ) = 2 2 π‘₯ s i n c o s s i n 2 2 .

  • A { 9 0 , 2 1 0 , 3 3 0 } ∘ ∘ ∘
  • B { 4 5 , 7 5 , 1 6 5 } ∘ ∘ ∘
  • C { 4 5 , 7 5 , 1 0 5 } ∘ ∘ ∘
  • D { 4 5 , 1 0 5 , 1 6 5 } ∘ ∘ ∘
  • E { 1 5 , 7 5 , 9 0 } ∘ ∘ ∘

Q13:

Find the solution set of given , where .

  • A
  • B
  • C
  • D