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MathematicsTrigonometric Ratios & IdentitiesMaximum & Minimum ValuesMedium2 minPYQ_2021

MathematicsMediumnumerical

The number of integral values of $k$ for which the equation $3 \sin x + 4 \cos x = k + 1$ has a solution, $k \in R$ is _______.

Answer:

11.00

Solution:

$3 \sin x + 4 \cos x = k + 1$

$\Rightarrow k + 1 \in [- \sqrt{3^{2} + 4^{2}}, \sqrt{3^{2} + 4^{2}}]$

$\Rightarrow k + 1 \in [- 5, 5]$

$\Rightarrow k \in [- 6, 4]$

No. of integral values of $k = 11$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Maximum & Minimum Values

⏱ 2mℹ️ Source: PYQ_2021

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