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Worksheet: Solving Equations Involving Secant, Cosecant, and Cotangent

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 πœƒ that satisfies c s c πœƒ βˆ’ √ 2 = 0 where πœƒ ∈ ο€» 0 , πœ‹ 2  .

Q2:

Find the value of πœƒ that satisfies c o t πœƒ βˆ’ √ 3 3 = 0 where πœƒ ∈ ο€» 0 , πœ‹ 2  .

Q3:

Find the value of πœƒ that satisfies c s c πœƒ βˆ’ 2 = 0 where πœƒ ∈ ο€» 0 , πœ‹ 2  .

Q4:

Find the value of πœƒ that satisfies s e c πœƒ βˆ’ 2 = 0 where πœƒ ∈ ο€» 0 , πœ‹ 2  .

Q5:

Find the set of values satisfying √ 3 πœƒ = 1 c o t given 0 < πœƒ < 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 } ∘ ∘

Q6:

Find the set of values satisfying c o t πœƒ = βˆ’ 1 given 0 < πœƒ < 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 } ∘ ∘

Q7:

Find the set of values satisfying s i n c o t πœƒ πœƒ = βˆ’ 1 2 where 0 ≀ πœƒ ≀ 9 0 ∘ ∘ .

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

Q8:

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

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

Q9:

Find πœƒ in degrees given s e c ( 1 8 0 + πœƒ ) = βˆ’ 2 √ 3 3 ∘ where πœƒ is the smallest positive angle.

Q10:

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

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