How do you explain sine and cosine?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What is the relationship between the unit circle and the sine graph?

Rotate the blue arrow around the unit circle.

How do you read sine and cosine functions?

Graphing Sine and Cosine Functions y = sin x and y = cos x There are two ways to prepare for graphing the basic sine and cosine functions in the form y = sin x and y = cos x: evaluating the function and using the unit circle. , and 2π for x and calculating the corresponding y value.

Why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine?

The reason that they are useful has to do with the properties of similar triangles. Similar triangles are triangles that have the same angle measures. All of these triangles have a hypotenuse of 1 , the radius of the unit circle. Their sine and cosine values are the lengths of the legs of these triangles.

What is sin on the unit circle?

Sine is opposite over hypotenuse. Since the hypotenuse is 1, sine on the unit circle is the opposite side. When you look at the unit circle, the opposite side is perpendicular to the x-axis. This means that, essentially, the opposite side is the height from, or the distance from, the x-axis, which is the y-value.

How do you tell the difference between a sine and cosine graph?

The graph of the cosine is the darker curve; note how it’s shifted to the left of the sine curve. The graphs of y = sin x and y = cos x on the same axes. The graphs of the sine and cosine functions illustrate a property that exists for several pairings of the different trig functions.

How do you interpret a cosine graph?

To graph the cosine function, we mark the angle along the horizontal x axis, and for each angle, we put the cosine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. It is the same shape as the cosine function but displaced to the left 90°.