Final answer:
The extreme values of the function sin(xπ/4) are -1 and 1. These values are the maximum and minimum that the sine function can achieve, while 0 is a value the sine function takes at specific points such as multiples of π. The value √2/2 is a value of sine at 45 and 135 degrees, not an extreme.
Step-by-step explanation:
The student is seeking to find the extreme values of the trigonometric function sin(xπ/4). Extreme values refer to the maximum and minimum values that a function can take. In the case of the sine function, it is well known that this function oscillates between -1 and 1, which are its extreme values. Additionally, sine can equal 0 when its argument is an integer multiple of π.
To find extreme values of sin(xπ/4), we consider the properties of the sine function. The sine of any angle is at its maximum when the angle is π/2 radians (90 degrees) and at its minimum when the angle is 3π/2 radians (270 degrees). So, the extreme values for the sine function are indeed -1 and 1, which correspond with the maximum and minimum, respectively. The sine function equals 0 at 0 radians (0 degrees), π radians (180 degrees), etc., where the term 'xπ/4' would be an integer multiple of π to satisfy this zero condition.
The correct answer to the question is therefore:
- a) -1
- b) 0
- c) 1
- d) √2/2 (this is not an extreme value but a specific value at π/4 and 3π/4 radians or 45 and 135 degrees)