Trigonometric EquationEasy
Question
If f : R → S defined by f(x) = sin x − √3 cos x + 1, is onto, then the interval of S is
Options
A.[0, 3]
B.[-1, 1]
C.[0, 1]
D.[-1, 3]
Solution
-2 ≤ sin x - √3 cos x ≤ 2 ⇒ - 1 ≤ sin x - √3 cos x + 1 ≤ 3
⇒ range of f(x) is [-1, 3].
Hence S is [-1, 3].
⇒ range of f(x) is [-1, 3].
Hence S is [-1, 3].
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