Lesson Worksheet: Solving a Trigonometric Equation Mathematics

In this worksheet, we will practice solving a trigonometric equation using factoring or squaring.


Find the set of values satisfying 4𝜃1=0cos given that 0<𝜃<180.

  • A{240,300}
  • B{120,240}
  • C{60,120}
  • D{60,300}
  • E{30,150}


If 0𝑥90, how many solutions are there of the equation 3𝑥=𝑥sintan?


How many solutions are there of the equation 3𝑥𝑥=𝑥sincossin if 0𝑥90?


Fill in the blank: If 0𝑥360, then the number of solutions of the equation 4𝑥=𝑥sintan is .


Find the set of values satisfying tantan𝜃+𝜃=0 where 0𝜃<360.

  • A{135,45,90,270}
  • B{135,315,0,180}
  • C{45,135,0,90}
  • D{135,225,0,180}


Find the set of values satisfying 22𝜃+2𝜃=0coscos given 0<𝜃360.

  • A{45,90,270,315}
  • B{0,45,135,180}
  • C{0,135,180,225}
  • D{90,135,225,270}


Find the set of values satisfying 3𝜃2𝜃𝜃=0sinsincos where 0𝜃<360. Give the answer to the nearest minute.

  • A{0,3341,180,14619}
  • B{0,14619,180,32619}
  • C{0,3341,180,21341}
  • D{0,14619,180,21341}


By first squaring both sides, or otherwise, solve the equation 4𝜃4𝜃=3sincos, where 0<𝜃360. Be careful to remove any extraneous solutions. Give your answers to two decimal places.

  • A𝜃=86.14,212.57
  • B𝜃=65.18,205.14
  • C𝜃=47.35,195.12
  • D𝜃=77.24,210.57
  • E𝜃=62.83,207.17


Find all the possible general solutions of 2𝜃2𝜃=0coscos.

  • A𝜋2+𝑛𝜋,𝜋2+𝑛𝜋,𝜋4+2𝑛𝜋,𝜋4+2𝑛𝜋𝑛:.
  • B𝜋2+2𝑛𝜋,𝜋2+2𝑛𝜋,𝜋4+2𝑛𝜋,𝜋4+2𝑛𝜋𝑛:.
  • C𝜋2+𝑛𝜋,𝜋4+2𝑛𝜋𝑛:.
  • D𝜋2+𝑛𝜋,𝜋4+2𝑛𝜋𝑛:.
  • E𝜋2+𝑛𝜋,𝜋4+2𝑛𝜋𝑛:.


Find all the possible solutions, that is, the general solution, of the equation sincossin𝜃𝜃=22𝜃.

  • A±𝜋4+2𝑛𝜋 (where 𝑛)
  • B𝑛𝜋, 𝜋2+2𝑛𝜋 (where 𝑛)
  • C𝑛𝜋, 𝜋4+2𝑛𝜋 (where 𝑛)
  • D𝑛𝜋, ±𝜋4+2𝑛𝜋 (where 𝑛)
  • E𝑛𝜋, ±𝜋2+2𝑛𝜋 (where 𝑛)

This lesson includes 19 additional questions and 187 additional question variations for subscribers.

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