Lesson Worksheet: Solving Reciprocal Trigonometric Equations Mathematics

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}∘∘

Q12:

Find the set of values of 𝜃 that satisfies cotsincsc𝜃𝜃=𝜃, where 𝜃∈[0,360]∘∘.

  • A{225,315}∘∘
  • B{0,45}∘∘
  • C{45,135}∘∘
  • D{0,225}∘∘
  • E{45,225}∘∘

Q13:

Find the values of 𝜃 that satisfy √3(𝜃)+3(𝜃)(𝜃)=0cottancot, where 𝜃∈[0,360]∘∘.

  • A30∘, 150∘
  • B∅
  • C150∘, 330∘
  • D30∘, 120∘
  • E150∘, 210∘

Q14:

Find the solution set of 𝜃 that satisfies cot𝜃−√3=0, where 𝜃∈[180,270]∘∘

Q15:

Find the solution set of 𝜃 that satisfies sec(−𝜃)=1, where 𝜃∈[0,90]∘∘.

Q16:

Find the solution set of 𝜃 that satisfies sec(𝜃)=−√2 given that 0≤𝜃<360∘∘.

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

Q17:

Find the set of values satisfying √3(𝜃)−2=0csc given that 0≤𝜃<360∘∘.

  • A{120,240}∘∘
  • B{60,300}∘∘
  • C{30,120}∘∘
  • D{60,120}∘∘
  • E{240,300}∘∘

Q18:

Find the set of values satisfying 2(𝜃)(𝜃)+(𝜃)(𝜃)=0sincscseccot given that 0≤𝜃<360∘∘.

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

Q19:

Find 𝜃 in degrees given that tan(90+𝜃)=−1∘, where 𝜃 is the smallest positive angle.

Q20:

Find 𝜃 in degrees given that cot(180−𝜃)=1∘, where 𝜃 is the smallest positive angle.

  • A45∘
  • B30∘
  • C225∘
  • D315∘
  • E135∘

Q21:

Find 𝜃 in degrees given that sec(180−𝜃)=2, where 𝜃 is the smallest positive angle.

Q22:

Find 𝜃 in degrees given that sec(90−𝜃)=2∘, where 𝜃 is the smallest positive angle.

Q23:

Find the solution set of 𝜃 that satisfies √3(90−𝜃)−2=0csc∘, where 𝜃∈[0,180]∘∘.

  • A{30}∘
  • B{60}∘
  • C{150}∘
  • D{45}∘
  • E{120}∘

Q24:

Find the solution set of 𝜃 that satisfies 2𝜃𝜃−1=0tansec, where 0<𝜃<360∘∘.

  • A{330}∘
  • B{30}∘
  • C{30,150}∘∘
  • D{150}∘
  • E{210,330}∘∘

Q25:

Find the values of 𝜃 that satisfy 2𝜃𝜃𝜃=1seccossin, where 0<𝜃<360∘∘.

  • A45,135∘∘
  • B30,150∘∘
  • C225,315∘∘
  • D∅
  • E210,330∘∘

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