Question

the domain (input values) of the sine function is: a. angle measures between 0 and π radians. b. angle measures between 0 and 2π radians. c. all angle measures, including negative angles. d. angle measures less than 90°.

Explanation:

The sine function \( y = \sin(x) \) is defined for all real numbers \( x \), where \( x \) represents angle measures (in radians, or can be converted from degrees). This means the domain includes all positive, negative, and zero angle measures. Option A limits to \( 0 \) to \( \pi \), Option B to \( 0 \) to \( 2\pi \) (these are intervals for the principal or a single period, not the entire domain), and Option D limits to less than \( 90^\circ \) (which is too restrictive). Only Option C correctly states that the domain is all angle measures, including negative angles.

Answer:

C. all angle measures, including negative angles.