Final answer:
The value -π/3 is indeed related to sin(x) since the sine function's domain includes all real numbers. The specific value for sin(-π/3) is -√3/2. Real-world phenomena like ocean waves may not always follow a perfect sinusoidal pattern. The correct option is B .
Step-by-step explanation:
Is -π/3 related to sin(x)? The correct answer is a) Yes. The sine function, denoted as sin(x), is a fundamental trigonometric function that describes the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle. However, the domain of sin(x) is all real numbers, which means that it accepts any real number, including negative ones and multiples of π. Therefore, -π/3 is indeed related to the sine function.
The value of sin(x) when x is -π/3 can be computed as follows:
- Recall that the unit circle is a circle with a radius of one centered at the origin of the coordinate system and is often used to define sine and cosine functions for all real numbers.
- Angle -π/3 corresponds to an angle of 120 degrees when measured in a clockwise direction (since it is negative) from the positive x-axis.
- For the angle -π/3, the sine value is equivalent to the y-coordinate of the point on the unit circle where the terminal side of the angle intersects the circle.
- The y-coordinate at this angle is -√3/2, therefore sin(-π/3) = -√3/2.
The sine function can describe various periodic phenomena, including sound waves and ocean waves. However, it's important to note that not all waves are perfectly sinusoidal. For instance, ocean waves are influenced by factors such as wind, tides, and underwater topography and, as a result, may not always form a perfect sinusoidal shape. Therefore, while sinusoidal functions are used in modeling waves, this is an idealization, and real-world wave patterns can be far more complex.