Quadratic Trigonometric Equations

A quadratic trigonometric equation is any equation with a orterm, or aorterm, since these become quadratic on using the appropriate double angle identity.

The solutions of trigonometric equations can be found by factorisation or using the quadratic formula. Generally the roots are required in an interval of 360 ° - either [0 °, 360 °] or [-180 °, 180 °] .

Example: Solve the equationfor the range 0 ° - 360 °.

Use the identityto obtain

This equation factorises to give

Now put each factor equal to 0 and solve.

Exaple: Solve the equation cos 2x = sin x in the interval [-180 °, 180 °] .

Use the identityto obtain

Move all the terms to one side to obtain

This expression factorises as

Put each factor equal to 0 and solve.