Final answer:
To determine the period of the function y=3.7sin(15x)−0.1, we use the formula Period = 2π/B, which gives Period = π/7.5 or approximately 0.419. The provided answer choices do not match this calculation, indicating a possible error in the question or answer options.
Step-by-step explanation:
The question asks to determine the period of the function y=3.7sin(15x)−0.1 without graphing. In a sine function of the form y = A sin(Bx + C) + D, the period can be calculated using the formula Period = π/B or Period = 2π/B when measuring in radians. Since we are provided with y=3.7sin(15x)−0.1 and B = 15, the correct period formula is Period = 2π/15. When you perform the calculation, this simplifies to Period = π/7.5 or approximately 0.419 when using π≈ 3.14159265. However, since the options given in the question are 24, 15, 30, and 3.7, which are not close to 0.419, there could be an error in the question itself or the options provided. The typical period formula is not resulting in one of the given answer choices.