Question

Determine the minimum and maximum value of the following trigonometric function:

f(x) = 10 cos(1/4x)
A. Minimum: -10, Maximum: 10
B. Minimum: -5, Maximum: 5
C. Minimum: -1, Maximum: 1
D. Minimum: 0, Maximum: 10

Answer 1

The minimum and maximum values of the function f(x) = 10 cos(1/4x) are -10 and 10, respectively, as the cosine function ranges between -1 and 1, and is multiplied by 10.

Step-by-step explanation:

To find the minimum and maximum value of the trigonometric function f(x) = 10 cos(1/4x), we need to consider the properties of the cosine function. The cosine function takes on values between -1 and 1, inclusive. When multiplying this by 10, the range of values becomes -10 to 10. Therefore, the minimum value of the function is when cos(1/4x) is -1, resulting in f(x) being -10. Conversely, the maximum value is when cos(1/4x) is 1, making f(x) equal to 10. Thus, the minimum and maximum values are -10 and 10 respectively.