This cheat sheet covers the high school math concept – Trigonometric Equations.
An equation, that involves trigonometric ratios of unknown angles, is known as a trigonometric equation. The values of the unknown angles that satify the equation are called the solutions to the equation.
In general, trigonometric equations end up having infinite solutions, due to the periodicity of the trigonometric functions. For example, if π/4 is a solution, then 2π + π/4, 4π + π/4, 6π + π/4, etc. are also the solutions of the equation. The set of all such solutions is called the general solution of the equation. In contrast, we can also find particular solutions to a trigonometric equation, which satifsy some other condition, say all solutions lying in the interval (-2π, 2π).
A good knowledge of the trigonometric ratios and basic identities is a must to understand and solve problems related to trigonometric equations. A cheat sheet on Trigonometry is also available on this website.
A decent understanding of graphs and their transformations will really help in quickly solving trigonometric equations. A cheat sheet on Graph Transformations is also available on this website.
This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.
The topics included in this cheat sheet are:
- Basic Trigonometric Equations: sinx = sinα, cosx = cosα, tanx = tanα, sin2x = sin2α, cos2x = cos2α, tan2x = tan2α
- Special Cases: sinx = 0, sinx = 1, sinx = -1, cosx = 0, cosx = 1, cosx = -1, tanx = 0, cotx = 0
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