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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.
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Why sine ratio is the ratio of opposite side and hypotenuse?
Because that is accepted definition. The sine is opposite over hypotenuse, or Y in the unit circle. The cosine is adjacent over hypotenuse, or X in the unit circle. The tangent is sine over cosine, etc. For more information, please see the related link below.
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
How the sine curve related to a curve?
Basically, it IS a curve.
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.
Why are sine functions such good models for repetitive behavior?
Repetitive behavior can be described by a point moving in a circle. The time of repetition is equivalent to time taken by that particle to complete that circle. When the point moves in a circle, its angle changes from 0 to 360 degrees; all of these values can be given by a sine function or a cosine function.
Why sine ratio is the ratio of opposite side and hypotenuse?
Because that is accepted definition. The sine is opposite over hypotenuse, or Y in the unit circle. The cosine is adjacent over hypotenuse, or X in the unit circle. The tangent is sine over cosine, etc. For more information, please see the related link below.
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.
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
What is the sine of 180?
The sine of 180 degrees is 0. Remember, the sine value on a unit circle is the y-value. If you find f(pi) in the function f(x)=sin(x), you will get zero as an answer.
Where can you find a 5 inch sine bar chart?
See related links for information about sine charts.
How the sine curve related to a curve?
Basically, it IS a curve.
How do you use the Pythagoras theorem in circle?
In a circle that has a radius of one you use Pythagorean theorem to derive the sine, cosine and tangent formulas. Draw a circle around the origin on graph paper. The sine is the line segment from the point where the side of the angle intersects down to the x-axis. etc.
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.
Why are sine functions such good models for repetitive behavior?
Repetitive behavior can be described by a point moving in a circle. The time of repetition is equivalent to time taken by that particle to complete that circle. When the point moves in a circle, its angle changes from 0 to 360 degrees; all of these values can be given by a sine function or a cosine function.
How are exponential and log functions related?
One is the inverse of the other, just like the arc-sine is the inverse of the sine, or division is the inverse of multiplication.
Properties of cosine and sine function?
The properties of the cosine and sine function are based on the X and Y coordinates of a point on a circle that has a radius of 1 and a center at the origin (X=0,Y=0). If the angle of the line from the origin to the edge of the circle, at any arbitrary point (X,Y), with respect to the X axis is theta, then sine(theta) is X, and cosine(theta) is Y.
Why sin angle equal to angle if the angle is very small?
The sine is almost equal to the angle, in case the angle is expressed in radians. Please make a picture of a circle, put a point on the circle at a small angle (say, 10 degrees or less), then draw the sine (a vertical line from the x-axis up to your point) for a small angle. You will see that the arc of the circle has almost the same length as the vertical line you drew. The arc is the angle; the vertical line is the sine.
