In two or more complete sentences, describe why the range of y = sin(x) is -1 ≤ y ≤ 1. make sure to reference the unit circle in your description.

The unit circle is a circle that is centered at the origin (0,0). The highest that it will go in terms of y is y = 1. The lowest y value is y = -1. So that's why y = sin(theta) is restricted in that manner. The sine function applies the ratio of the opposite site to the hypotenuse. For the unit circle, the hypotenuse is 1 since the radius is 1. Check out the image attachment for a reference drawing. The segment in red is the value of sin(theta) while the blue segment is the hypotenuse of 1. Dividing the red segment length over the blue segment length gets us sin(theta).

In short, the sine theta value is the height of the red segment point that sits on the unit circle. The highest that point goes is y = 1; the lowest it goes is y = -1.

The correct answer is:

The unit circle has a center at the origin (0, 0) and a radius with a length of one unit. The sine function has a minimum value of -1 and a maximum value of 1. The radius of the unit circle extends from the origin to (0,-1) and from the origin to (0,1).

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.