There are no universal rules. However, there are a number of situations : quadratic functions and their square roots for which trigonometric substitutions are effective.
Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
Google " volume of revolution " problems and see how integration makes these problems that would not be easily solved by other methods easier.
There are a few ways. First, there are a multitude of trigonometric tables which list the sines and cosines of a variety of values. if you now one trigonometric value of a number, you can find all the others by hand, and you can also use a Taylor series approximation to find a fairly accurate value. (In fact, many calculators use Taylor series to find trigonometric values.)
== Linear equations are those that use only linear functions and operations. Examples of linearity: differentiation, integration, addition, subtraction, logarithms, multiplication or division by a constant, etc. Examples of non-linearity: trigonometric functions (sin, cos, tan, etc.), multiplication or division by variables.
Use the trigonometric relations and identities.
Use trigonometric identities to simplify the equation so that you have a simple trigonometric term on one side of the equation and a simple value of the other. Then use the appropriate inverse trigonometric or arc function.
You can use them to find the sides and angles of a right triangle... just like regular trigonometric functions
Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.
There are many careers that use trigonometry:EngineersArchitectsArtistsPhysicistsAstronomersDraftsmanCraftsmanPharmacistFinancial Analyst
You only use the seccant trigonometric function.
trigonometric ratios for example you need at least 2 lenghts and 1 angle
The case of Rosa Parks extended integration and the use of buses by both races. It led to many protests which would eventually allow for full integration among all races across the country.
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
Google " volume of revolution " problems and see how integration makes these problems that would not be easily solved by other methods easier.
There are a few ways. First, there are a multitude of trigonometric tables which list the sines and cosines of a variety of values. if you now one trigonometric value of a number, you can find all the others by hand, and you can also use a Taylor series approximation to find a fairly accurate value. (In fact, many calculators use Taylor series to find trigonometric values.)
use of integration in electrical engineering