The minimum value of 3cosx + 4sinx + 8 is ______.

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Solution

The minimum value of 3cosx + 4sinx + 8 is 3.

Explanation:

The given expression is 3cosx + 4sinx + 8

Let y = 3cosx + 4sinx + 8

⇒ y – 8 = 3cosx + 4sinx

Minimum value of y – 8 = `sqrt((3)^2 + (4)^2`

⇒ y – 8 = `-sqrt(9 + 16)` = – 5

⇒ y = 8 – 5 = 3

So, the minimum value of the given expression is 3.

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Trigonometric Equations

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Q 41 Q 40 Q 42

Chapter 3: Trigonometric Functions - Exercise [Page 56]

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NCERT Exemplar Mathematics Exemplar [English] Class 11

Chapter 3 Trigonometric Functions
Exercise | Q 41 | Page 56

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