Question

Which statements are true about the functions y = sin(x), y = Cos(t), and y = tan(s)? 1. The domains et y = sin(t)-y = cos(I) and y = tan(t)-are-al real numbers: 2. Both y = sin(x) and y = tan(s) are increasing on the ∫erval (0, 3), and y = cos(a) is decreasing on that ∫erval. 3. The amplitudes of y = sin(s), y = cos(x), and y = tan(s) are 1. 4. The graphs of y = sin(x) and y cos(1) do not have midlines. 5. The periods of y = sin(x) and y = cos(s) are 277, and the period of y = tan(t).

Answer 1

The correct statements about the sinusoidal functions are

• Both y = sin(x) and y = tan(x) are increasing on the interval (0, π/2), while y = cos(x) is decreasing on the same interval (Option 2).
• The periods of y = sin(x) and y = cos(x) are of 2π, while the period of y = tan(x) is of π (Option 5).

Step-by-step explanation:

The statements regarding the trigonometric functions are given as follows:

• The periods of y = sin(x) and y = cos(x) are 2π, while the period of y = tan(x) is π.
• Both y = sin(x) and y = tan(x) are increasing on the interval (0, π/2), while y = cos(x) is decreasing on the same interval.
• The amplitude of y = sin(x), y = cos(x), and y = tan(x) are 1 only for y = sin(x) and y = cos(x), as the tangent function does not have an amplitude.

Some of the statements provided need clarification:

1. The domain of y = tan(x) does not include all real numbers due to the asymptotes at odd multiples of π/2 where the function is undefined.
2. The midlines of y = sin(x) and y = cos(x) are the horizontal lines at y = 0, which serve as axes of symmetry for their respective wave functions.

Thus, the correct options are 2 and 5.

Your question is incomplete, but most probably your full question can be seen in the attachment.