Are the graphs of sin and cos identical?
The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values . The graphs of the two functions, though similar, are not identical. One way to describe their relationship is to say that the graph of is identical to the graph of shifted units to the left.
What are the 5 key points of a sine graph?
The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).
What is the graph of sine function?
To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.
What is the relationship between sine and cosine?
The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle.
How would you compare 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 .
Where do sine graphs start?
Plot of Sine The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.
At what value sine and cosine of an angle are equal?
A 45°–45°–90° triangle is an isosceles triangle, so the x- and y-coordinates of the corresponding point on the circle are the same. Because the x- and y-values are the same, the sine and cosine values will also be equal.
Does sin equal Cos?
In other words, the sine of an angle equals the cosine of its complement. Well, technically we’ve only shown this for angles between 0 ∘ and 90 ∘.
What do the graphs of sine and cosine have in common with the swing you see?
What do the graphs of sine and cosine have in common with the swinging you see? The high and low points repeat in pattern.
What is the relationship of sine and cosine?
Where does a sine graph start?
How would you describe the graphs of the sine and cosine functions?
The graph of y = sin x y = sin x is symmetric about the origin, because it is an odd function. The graph of y = cos x y = cos x is symmetric about the y y -axis, because it is an even function.