Worksheet: Solving Reciprocal Trigonometric Equations

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In this worksheet, we will practice solving trigonometric equations involving secant, cosecant, and cotangent over different intervals in degrees and radians.

Q1:

Find the value of 𝜃 that satisfies c s c 𝜃 − √ 2 = 0 where 𝜃 ∈ 0 , 𝜋 2 .

Q2:

Find the set of values satisfying √ 3 𝜃 = 1 c o t given 0 < 𝜃 < 3 6 0 ∘ ∘ .

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

Q3:

Find 𝜃 in degrees given s e c ( 1 8 0 + 𝜃 ) = − 2 √ 3 3 ∘ where 𝜃 is the smallest positive angle.

Q4:

Find the set of values satisfying s i n c o t 𝜃 𝜃 = − 1 2 where 0 ≤ 𝜃 ≤ 9 0 ∘ ∘ .

  • A { 1 8 0 , 1 3 5 } ∘ ∘
  • B { 3 0 , 3 3 0 } ∘ ∘
  • C { 3 0 , 1 8 0 } ∘ ∘
  • D ∅

Q5:

Find the value of 𝜃 that satisfies c o t 𝜃 − √ 3 3 = 0 where 𝜃 ∈ 0 , 𝜋 2 .

Q6:

Find the value of 𝜃 that satisfies c s c 𝜃 − 2 = 0 where 𝜃 ∈ 0 , 𝜋 2 .

Q7:

Find the value of 𝜃 that satisfies s e c 𝜃 − 2 = 0 where 𝜃 ∈ 0 , 𝜋 2 .

Q8:

Find the set of values satisfying c o t 𝜃 = − 1 given 0 < 𝜃 < 3 6 0 ∘ ∘ .

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

Q9:

Find the set of values satisfying s i n c o t 𝜃 𝜃 = √ 2 2 where 0 ≤ 𝜃 < 3 6 0 ∘ ∘ .

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

Q10:

Find 𝜃 in degrees given c o t ( 1 8 0 + 𝜃 ) = 1 ∘ where 𝜃 is the smallest positive angle.

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