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Worksheet: Solving Trigonometric Equations

Q1:

Find the value of 𝑋 given t a n ο€Ό 𝑋 4  = √ 3 where 𝑋 4 is an acute angle.

Q2:

Find the value of 𝑋 given s i n ο€Ό 𝑋 3  = √ 3 2 where 𝑋 3 is an acute angle.

Q3:

Find the set of values satisfying c o s ( πœƒ βˆ’ 1 0 5 ) = βˆ’ 1 2 where 0 < πœƒ < 3 6 0 ∘ ∘ .

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

Q4:

Find the set of values satisfying c o s ( πœƒ βˆ’ 2 8 ) = 1 √ 2 where 0 < πœƒ < 3 6 0 ∘ ∘ .

  • A { 8 8 , 3 2 8 } ∘ ∘
  • B { 2 8 , 5 8 } ∘ ∘
  • C { 3 2 , 8 8 } ∘ ∘
  • D { 7 3 , 3 4 3 } ∘ ∘

Q5:

Find the set of values satisfying s i n ο€½ 1 5 πœƒ 7  = 1 √ 2 given 0 < 1 5 πœƒ 7 < 3 6 0 ∘ ∘ .

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

Q6:

Find the set of values satisfying s i n ο€½ 5 πœƒ 2  = √ 3 2 given 0 < 5 πœƒ 2 < 3 6 0 ∘ ∘ .

  • A { 4 8 } ∘
  • B { 2 4 } ∘
  • C { 6 0 , 1 2 0 } ∘ ∘
  • D { 2 4 , 4 8 } ∘ ∘
  • E { 2 0 4 , 3 3 6 } ∘ ∘

Q7:

Find πœƒ in degrees given c o s ( 9 0 + πœƒ ) = βˆ’ 1 2 ∘ where πœƒ is the smallest positive angle.

Q8:

Find πœƒ in degrees given s i n ( 9 0 + πœƒ ) = √ 3 2 ∘ where πœƒ is the smallest positive angle.