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 csc𝜃2=0 where 𝜃0,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)=233 where 𝜃 is the smallest positive angle.

Q4:

Find the set of values satisfying sincot𝜃𝜃=12 where 0𝜃90.

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

Q5:

Find the value of 𝜃 that satisfies sec𝜃2=0 where 𝜃0,𝜋2.

Q6:

Find the value of 𝜃 that satisfies sec𝜃233=0 where 𝜃0,𝜋2.

Q7:

Find the value of 𝜃 that satisfies csc𝜃233=0 where 𝜃0,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 0𝜃<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 0𝜃<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 cot𝜃3=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 0𝜃<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 0𝜃<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 0𝜃<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(180𝜃)=1, where 𝜃 is the smallest positive angle.

  • A45
  • B30
  • C225
  • D315
  • E135

Q21:

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

Q22:

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

Q23:

Find the solution set of 𝜃 that satisfies 3(90𝜃)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 2𝜃𝜃1=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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