Study Tips: Finding Values For Trigonometric Identities

With this tip, you will learn:

  • The 4 types of trigonometric identities

  • The formulae to find maximum & minimum values for trigonometric identities for each type

  • An example problem to solve

What are the different types of trigonometric identities?

Type 1: a sinx±b cosx ; a sinx±b sinx ; a cosx±b cosx

The values of these kind of identities is given as,
Minimum : - sqrt(a^2 + b^2)
Maximum: + sqrt(a^2 + b^2)

Type 2: (sinx cosx)^n

The values of these kind of identities is given as,
Minimum : (1/2)^n
Maximum: Value can go upto infinity

Type 3: a sin^2 x + b cos^2 x

The values of these kind of identities is given as follows:
(If a > b) Minimum : b
Maximum: a

(If a < b) Minimum : a
Maximum: b

Type 4: a sin^2 x + b cosec^2 x ; a cos^2 x + b sec^2 x ; a tan^2 x ± b cot^2 x

The values of these kind of identities is given as,
Minimum : 2.sqrt(ab)
Maximum: Value can go upto infinity

Note : These formulae can only be applied once the expression has been deduced to appear like any one of the above types.



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How can I solve problems where a constant C is present?

For example, if you are asked to find out the maximum and minimum values for the expression, 4sinx + 3cosx + 5, then you have to apply the Type-1 formula.

Then, according to the formula:
Maximum value for the expression is,
= sqrt(4^2+3^2) + 5
= 5 + 5
= 10


Minimum value for the expression is,
= sqrt(4^2+3^2) - 5
= 5 - 5
= 0

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