Worksheet: Solving Reciprocal Trigonometric Equations

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}

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