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 csc𝜃−√2=0 where 𝜃∈0,𝜋2.

Q2:

Find the set of values satisfying √3𝜃=1cot given 0<𝜃<360∘∘.

  • A{300,240}∘∘
  • B{120,300}∘∘
  • C{60,300}∘∘
  • D{60,240}∘∘

Q3:

Find 𝜃 in degrees given sec(180+𝜃)=−2√33∘ where 𝜃 is the smallest positive angle.

Q4:

Find the set of values satisfying sincot𝜃𝜃=−12 where 0≤𝜃≤90∘∘.

  • A{30,330}∘∘
  • B∅
  • C{30,180}∘∘
  • D{180,135}∘∘

Q5:

Find the value of 𝜃 that satisfies sec𝜃−2=0 where 𝜃∈0,𝜋2.

Q6:

Find the value of 𝜃 that satisfies sec𝜃−2√33=0 where 𝜃∈0,𝜋2.

Q7:

Find the value of 𝜃 that satisfies csc𝜃−2√33=0 where 𝜃∈0,𝜋2.

Q8:

Find the set of values satisfying cot𝜃=−1 given 0<𝜃<360∘∘.

  • A{135,225}∘∘
  • B{225,315}∘∘
  • C{45,225}∘∘
  • D{135,315}∘∘

Q9:

Find the set of values satisfying sincot𝜃𝜃=√22 where 0≤𝜃<360∘∘.

  • A∅
  • B{45,315}∘∘
  • C{120,90}∘∘
  • D{180,30}∘∘

Q10:

Find 𝜃 in degrees given sin(180+𝜃)=−√32∘ where 𝜃 is the smallest positive angle.

Q11:

Find the set of values satisfying 2𝜃+𝜃𝜃=0sincossec where 0≤𝜃<360∘∘.

  • A{30,150}∘∘
  • B{240,300}∘∘
  • C{210,330}∘∘
  • D{60,120}∘∘

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