Determine whether the following statement is true or false. The maximum value of the function \( y=-2 \cos x+4 \) is 8 . Is the statement true or false? True. False, the maximum value is 1 . False, the maximum value is 6 . False, the maximum value is 4 .

To determine whether the statement is true or false, we first analyze the function \( y = -2 \cos x + 4 \). The cosine function oscillates between -1 and 1. Therefore, \( -2 \cos x \) oscillates between -2 and 2. Adding 4 shifts this range up: When \( \cos x = -1 \): \[ y = -2(-1) + 4 = 2 + 4 = 6 \] When \( \cos x = 1 \): \[ y = -2(1) + 4 = -2 + 4 = 2 \] Thus, the maximum value of the function is 6, making the correct option: **False, the maximum value is 6.** If you're excited about cosine functions, they have a rich history in mathematics! Did you know that ancient Greeks used them to study music theory? The rhythmic waves of sound led to early concepts of trigonometry! And when considering the real-world applications, trigonometric functions like cosine play critical roles in engineering and physics—think waves, oscillations, and even satellite communication! Without these, our modern tech would be lost!