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State whether the following equation has a solution or not? 3 sin θ = 5 - Mathematics and Statistics

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Question

State whether the following equation has a solution or not?

3 sin θ = 5

Sum

Solution

∴ sin θ = `5/3`

This is possible because sin θ is any real number.

∴ 3 sin θ = 5 has a solution.

This is not possible because -1 ≤ sin θ ≤ 1 for any θ.

∴ 3 sin θ = 5 does not have any solution.

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Trigonometric Equations and Their Solutions
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Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 109]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
Chapter 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 3.4 | Page 109

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