What do the values on the unit circle mean?
What do the values on the unit circle mean?
The x-coordinate represents the distance traveled left or right from the center. The y-coordinate represents the distance traveled up or down. The x-coordinate is the cosine of the angle formed by the point, the origin and the x-axis. The y-coordinate is the sine of the angle.
What is the radius of a unit circle?
1
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Is sin an XR or a yr?
THE UNIT CIRCLE
| sin θ | = | y r |
|---|---|---|
| cos θ | = | x r |
| tan θ | = | y x |
Is Tan y x or x y?
The tangent of theta is defined to be y over x where y and x are these coordinates. So the second coordinate divided by the first coordinate, that’s the tangent of theta.
Where is sin 0 on unit circle?
On the unit circle, the x-coordinate at each position is the cosine of the given angle, and the y-coordinate is the sine. For θ=0 , the rightmost point, the coordinate pair is (1, 0). The y-coordinate is 0, so sin(0)=0 .
Is tangent cos sin?
The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x .
Why is cosine x r?
Recall that r measures the distance from the point (x, y) ≠ (0, 0) lying on the terminal side of an angle in standard position to the origin. Thus, cos θ = x/ r and sin θ = y/r cannot be greater than 1 or less than −1, depending on whether x and y are positive or negative (r = x when y = 0 and r = y when x = 0).
Where is cosine positive?
All the trig functions are positive in Quadrant 1. Sine and cosecant are positive in Quadrant 2, tangent and cotangent are positive in Quadrant 3, and cosine and secant are positive in Quadrant 4.
