Find the Range y=3/2*cos(t/2)

Problem

y=3/2*cos(t/2)

Solution

1. Identify the parent function and its range. The basic cosine function cos(θ) oscillates between −1 and 1 for all real values of θ

θ=t/2

−1≤cos(t/2)≤1

2. Apply the vertical stretch. The coefficient 3/2 represents the amplitude of the function, which scales the output values of the cosine function.

−1⋅3/2≤3/2*cos(t/2)≤1⋅3/2

3. Simplify the inequality to determine the minimum and maximum values of y

−3/2≤y≤3/2

4. Determine the range in interval notation. Since the function reaches both its minimum and maximum values, the range includes all values from −3/2 to 3/2

Range=[−3/2,3/2]

Final Answer

Range of *y=3/2*cos(t/2)* is *[−3/2,3/2]

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