Maths > Trigonometric Equations and Inequalities > 4.0 Trigonometric Inequalities
Trigonometric Equations and Inequalities
1.0 Definition
2.0 General Solution of Trigonometric Functions
3.0 Steps to solve trigonometric equations of the form$$a\cos \theta + b\sin \theta = c$$
4.0 Trigonometric Inequalities
5.0 Period of trigonometric function
4.1 Steps in solving trigonometric inequalities
To solve any trigonometric inequality $f(x)>0$ or $f(x)<0$, first consider it without inequality and equivalent to $f(x)=0$. Solve it to get all of its real roots using various transformation identities explained in the previous chapter and then find the intervals of $x$ as per the inequality sign is given in the question.
Basic steps to solve trigonometric inequalities are:
- Transform the given trigonometric inequality $f(x)>/<0$ into standard form using various transformation identities.
- Find the common period.
- Solve the trigonometric equation $f(x)=0$ and find the values of $x$ satisfying the equation.
- Solve the inequality $f(x)>/<0$ using algebraic method.
Before proceeding further we should concentrate on the second step in which we need to find the common period.
