Quadratic Trigonometric Equations (DP IB Maths: AA SL)

How are quadratic trigonometric equations solved?

• A quadratic trigonometric equation is one that includes either , or 
• Often the identity can be used to rearrange the equation into a form that is possible to solve
  • If the equation involves both sine and cosine then the Pythagorean identity should be used to write the equation in terms of just one of these functions
• Solve the quadratic equation using your GDC, the quadratic equation or factorisation
  • This can be made easier by changing the function to a single letter
    • Such as changing  to 
• A quadratic can give up to two solutions
  • You must consider both solutions to see whether a real value exists
  • Remember that solutions for sin θ = k and cos θ = k only exist for -1 ≤ k ≤ 1  
  • Solutions for tan θ = k exist for all values of k
• Find all solutions within the given interval
  • There will often be more than two solutions for one quadratic equation
  • The best way to check the number of solutions is to sketch the graph of the function