Find the range of (5 sin θ + 4).

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Domain and Range of Trigonometric Functions, Graph of Sine Function | PadhAiPro

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TextDomain and Range of Trigonometric FunctionsGraph of Sine Function

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Assertion (A) : For matrix A = [1 cos θ 1; – cos θ 1 cos θ; – 1 – cos θ 1], where θ ∈ [0, 2π], |A| ∈ [2, 4]. Reason (R) : cos θ ∈ [– 1, 1], ∀ θ ∈ [0, 2π].

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Find the domain of the function f(x) = sin⁻¹(x² – 4). Also, find its range.

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Assertion (A): Maximum value of (cos⁻¹ x)² is π². Reason (R): Range of the principal value branch of cos⁻¹x is [-π/2, π/2].

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Assertion (A) : The principal value of cot⁻¹(−√3) is π/6. Reason (R) : Domain of cot⁻¹ x is ℝ − {−1, 1}.

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