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There are no universal rules. However, there are a number of situations : quadratic functions and their square roots for which trigonometric substitutions are effective.

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Q: When would you use Integration by Trigonometric Substitution?
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How do use substitution when solving system of equations?

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.


How do you find trigonometric ratios without a calculator?

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.)


What is the use of integration in your practical life?

Google " volume of revolution " problems and see how integration makes these problems that would not be easily solved by other methods easier.


How would use solve the system of equation x plus 3y equals 23 by using substitution?

You'd need another equation to sub in


What is a reciprocal trig function?

A reciprocal trigonometric function is the ratio of the reciprocal of a trigonometric function to either the sine, cosine, or tangent function. The reciprocal of the sine function is the cosecant function, the reciprocal of the cosine function is the secant function, and the reciprocal of the tangent function is the cotangent function. These functions are useful in solving trigonometric equations and graphing trigonometric functions.