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1. If 0≤x≤ π/2, What is the maximum value of cos (x/3)?
- A. 1
- B. 1
- C. 1
- D. 1
Answer: Option A
Explanation:
o find the maximum value of cos(x/3) when 0 ≤ x ≤ π/2, we can analyze the properties of the cosine function.
The cosine function reaches its maximum value of 1 when the argument (angle) is 0. In this case, the argument is x/3.
Since 0 ≤ x ≤ π/2, we have 0 ≤ x/3 ≤ π/6 (because π/6 is one-sixth of π/2). In this range, cos(x/3) will be maximized when x/3 = 0, which means x = 0.
So, the maximum value of cos(x/3) is cos(0) = 1.
Therefore, the maximum value of cos(x/3) when 0 ≤ x ≤ π/2 is 1.
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