Trigonometric Ratios and Identities
Range of Trigonometric Functions
JEE Main 2021
Grade 11
Question:
Find the number of integral values of $k$ for which the equation $3 \sin x + 4 \cos x = k + 1$ has a real solution.
Step-by-Step Solution
Key Concept: The maximum of $3 \sin x + 4 \cos x$ is $\sqrt{9 + 16} = 5$ and the minimum is $-5$. For a solution, $k + 1$ must lie in $[-5, 5]$. Count the integers $k$ satisfying this.
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Correct Answer: 11