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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
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.
How the sine curve related to a curve?
Basically, it IS a curve.
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.
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 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 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 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.
How the sine curve related to a curve?
Basically, it IS a curve.
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.
What is the sine of a 90 degree angle?
The sine of a 90-degree angle is equal to 1. This is because, in the unit circle, a 90-degree angle corresponds to the point (0, 1), where the sine is defined as the y-coordinate. Thus, sin(90°) = 1.
What does sine in trigonometry mean?
In trigonometry, sine is a fundamental function that relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the hypotenuse. It is commonly denoted as sin(θ), where θ is the angle in question. The sine function is also defined for all real numbers using the unit circle, where it represents the y-coordinate of a point on the circle corresponding to that angle. Sine is widely used in various applications, including physics, engineering, and signal processing.
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.
