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Sine is NOT the y coordinate: it is the sine of the angle made by the x-axis and the radius from a point on the circle. It is the cosine of the angle made with the y-axis.
Consider any point, P, on the unit circle with coordinates (x, y). And let Q be the foot of the perpendicular from P to the x-axis. Then y = PQ.
Now, in the right angled triangle OPQ, if OP makes an angle theta with the x axis, then sin(theta) = PQ/OP = y/OP and since OP is the radius of a unit circle, OP = 1 so that sin(theta) = y.
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How do you write an equation for a circle with a center?
Equation of any circle, with any radius, and its center at any point: [ x - (x-coordinate of the center) ]2 + [ y - (y-coordinate of the center) ]2 = (radius of the circle)2
In trig how is the value of r interpreted geometrically in the definitions of the sine cosine secant and cosecant?
In trigonometry, the value of R is the radius of the circle, and is usually normalized to a value of 1. If the circle is at the X-Y origin, and theta is the angle between the radius line R, and X and Y are the X and Y coordinates of the point on the circle at the radius line, then... sine(theta) = Y / R cosine(theta) = X / R secant(theta) = 1 / cosine(theta) = R / X cosecant(theta) = 1 / sine(theta) = R / Y
Find all the coordinates of the points on unit circle?
If x2 + y2 = 1, then the point (x,y) is a point on the unit circle.
You can find the rise by the y-coordinate of the left point from the y-coordinate of the right point?
subtracting
What is the name of the x and y in an ordered pair?
The first and second coordinate. X is the first coordinate and y is the second.
How is the unite circle related to sine?
If you draw a unit circle, the sine function can be expressed as the y-coordinate of a point on the circle; the cosine function as the x-coordinate.
How does the unit circle relate to sin cos and tan?
Sine: the y-coordinate. Cosine: the x-coordinate. Tangent: the ratio of the two (y/x).
On the unit circle define the sine function by using the distance walked as the input and the y coordinate as the output?
Yes, but only if the argument of the sine function is in radians.
What is a sine in mathematics?
A function that depends on the value of an angle. One way to define it is with a unit circle (a circle with center in the coordinate origin, and radius of 1). To the right is zero, from there, a positive angle is counterclockwise. In this case, the sine is simply the y-coordinate, and the cosine is the x-coordinate of the point on the circle where the ray of the angle crosses the circle. The value of the sine (and cosine) obviously depends on the angle - that's why it is considered a "function". Sine, cosine, tangent, cotangent, cosecans, and secans can also be defined via right triangles; for more details see here: http://en.wikipedia.org/wiki/Sine#Sine.2C_cosine_and_tangent
Why is it cosine 90 degrees is 0?
It helps to think as the sine and cosine as coordinates of a unit circle - a circle of radius 1, with center at the origin of the coordinates, i.e., point (0, 0). In this case, as you go around on the circle (starting at the right, coordinates (1, 0), and going counterclockwise), the cosine of the angle is simply the x-coordinate, and the sine of the angle is simply the y-coordinate. At 90°, the x-coordinate is 0, therefore the cosine is 0. Also, at 90° the y-coordinate is 1, therefore the sine is 1 (that's the maximum value it can have).
What is e meaning sin tan and cos?
sin is short for sine, cos for cosine, tan for tangent. These functions are defined in several ways; one way is with a unit circle - a circle with radius 1, in which angles are measured starting on the right, and then counterclockwise. In this case, the sine is the y-coordinate on the circle - as a function of the angle. For example, for an angle of 0°, the y-coordinate is 0; for an angle of 90°, the y-coordinate is 1. Therefore, the sine of 0° is said to be zero, and the sine of 90° is said to be one. Similarly, the cosine is the x-coordinate. The tangent of x is the ratio of sine x / cosine x. - Note that in advanced math, angles are often measured in radians instead of the (rather arbitrary) degrees.
What is coordinates of points in the unit circle?
I'm not sure exactly what this question is asking, but I will attempt to answer. An angle on the unit circle is created by drawing a straight line from the origin to a point on the circle. The x-coordinate of a point corresponds to the cosine of the angle. For example: cos(90o) = 0 The y-coordinate of a point corresponds to the sine of the angle. For example: sin(270o) = -1
How do you prove sin90equalsto 1?
Make a diagram. One way to define sine and cosine is with the unit circle - a circle with a radius of 1 unit. For any point on the circle, the sine is the y-component, while the cosine is the x-component.
Why does cos negative theta equal cos postitive theta?
The cosine is simply the x-coordinate of the unitary circle. It helps to draw the circle, and the sine and cosine (x and y coordinates), to visualize this. The y-coordinate is the same for a positive angle and for the corresponding negative angle.
Why is it impossiple for an angle to have a sine larger than 1?
sin(theta) is the y-coordinate of the intersection of a line forming an angle with the positive x-axis and the unit circle (i.e., circle of radius one, centered at the origin). The unit circle has its highest y-value at the point (0,1). Drawing the unit circle on a graph makes this obvious. Assume that there were a higher y-value than one possible. y>1 --> y2>1. Because x2>=0 for all real x, y2>1 --> x2+y2>1, which is impossible for a point on the unit circle (since for all points on the unit circle (x,y), x2+y2=1).
What is the equation of a unit circle?
A unit circle is a circle of radius 1. If it's center is at the origin of an xy-coordinate system, then the equation is x (squared) + y (squared) = 1
Why cos negative results positive?
It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument. As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to define the sine and the cosine functions.)
