Pregunta
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Which of the following is true about the graph of the function \( f(x)=\sin (x) \) ? SELECT ALL THAT APPLY a The outputs are the sine value for the given rotation. b The inputs are the angle of rotation. c The input and output values come from the unit circle. dhe inputs are the sine value for the given rotation. e The outputs are the angle of rotation.

Ask by Watson Hardy. in the United States
Feb 27,2025

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The true statements about the graph of \( f(x) = \sin(x) \) are: - a. The outputs are the sine value for the given rotation. - b. The inputs are the angle of rotation. - c. The input and output values come from the unit circle.

Solución

To analyze the function \( f(x) = \sin(x) \), let's evaluate each statement one by one: a. **The outputs are the sine value for the given rotation.** - This statement is true. The function \( f(x) = \sin(x) \) gives the sine value for the angle \( x \) (in radians). b. **The inputs are the angle of rotation.** - This statement is also true. The input \( x \) represents the angle of rotation in radians. c. **The input and output values come from the unit circle.** - This statement is true as well. The sine function is defined based on the unit circle, where the input \( x \) corresponds to an angle, and the output \( f(x) \) corresponds to the y-coordinate of the point on the unit circle at that angle. d. **The inputs are the sine value for the given rotation.** - This statement is false. The inputs are angles, not sine values. e. **The outputs are the angle of rotation.** - This statement is false. The outputs are the sine values, not the angles. Based on this analysis, the true statements about the graph of the function \( f(x) = \sin(x) \) are: - a. The outputs are the sine value for the given rotation. - b. The inputs are the angle of rotation. - c. The input and output values come from the unit circle.

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The Deep Dive

a The outputs are the sine value for the given rotation. b The inputs are the angle of rotation. c The input and output values come from the unit circle. These statements accurately describe the function \( f(x)=\sin (x) \), where inputs correspond to angles measured in radians, and the outputs represent the sine values of those angles. The relationship between the sine function and the unit circle is foundational in trigonometry!

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