If the equation contains trig functions with the same angle and some of them are squared then it may be possible to use a Pythagorean identity to write an equation in the same trig. function which may then possibly factorise.

In these examples I show you how the Pythagorean identities help solve some equations.

Pythagorean Identities:

  •     \[{{{\sin }^2}\theta  + {{\cos }^2}\theta  \equiv 1}\]

  •     \[{1 + {{\tan }^2}\theta  \equiv {{\sec }^2}\theta }\]

  •     \[{1 + {{\cot }^2}\theta  \equiv {\rm{cose}}{{\rm{c}}^2}\theta }\]

Solve:

  1. 2\sin 2\theta  + 8{\cos ^2}2\theta  = 5 \text{ for } {0^ \circ } \le \theta  \le {360^ \circ }

Solve:

  1. 2{\sec ^2}\theta  + \tan \theta  = 3 \text{ for } 0 \le \theta  \le 2\pi

Solve:

  1. \dfrac{2}{{{{\tan }^2}\theta }} + 8 = 7{\rm{cosec }}\theta \text{ for } \[0 \le \theta  \le \pi

Recent Posts