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In a right angled triangle, the sine of an angle is: The length of the side opposite the angle divided by the length of the hypotenuse. The abbreviation is sin sin θ = opposite / hypotenuse.
- Sine, Cosine, Tangent
Sine, Cosine and Tangent (often shortened to sin, cos and...
- The Law of Sines
The Law of Sines (or Sine Rule) is very useful for solving...
- Sine, Cosine, Tangent
- Right Triangle
- Sine, Cosine and Tangent
- Size Does Not Matter
- Angles from 0° to 360°
- Why?
- Exercise
- Less Common Functions
Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a nameto each side of a right triangle:
Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sidesof a right angled triangle: For a given angle θ each ratio stays the same no matter how big or small the triangle is To calculate them: Divide the length of one side by another side
The triangle can be large or small and the ratio of sides stays the same. Only the angle changes the ratio. Try dragging point "A" to change the angle and point "B" to change the size: Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. But you still need to remember what they mean! I...
Move the mouse around to see how different angles (in radians or degrees) affect sine, cosine and tangent. In this animation the hypotenuse is 1, making the Unit Circle. Notice that the adjacent side and opposite side can be positive or negative, which makes the sine, cosine and tangent change between positive and negative values also.
Why are these functions important? 1. Because they let us work out angles when we know sides 2. And they let us work out sides when we know angles
Try this paper-based exercisewhere you can calculate the sine functionfor all angles from 0° to 360°, and then graph the result. It will help you to understand these relativelysimple functions. You can also see Graphs of Sine, Cosine and Tangent. And play with a spring that makes a sine wave.
To complete the picture, there are 3 other functions where we divide one side by another, but they are not so commonly used. They are equal to 1 divided by cos, 1 divided by sin, and 1 divided by tan:
This page explains the sine, cosine, tangent ratio, gives on an overview of their range of values and provides practice problems on identifying the sides that are opposite and adjacent to a given angle. The Sine, Cosine and Tangent functions express the ratios of sides of a right triangle.
Sine. Sine, written as sin(θ), is one of the six fundamental trigonometric functions. Sine definitions. There are two main ways in which trigonometric functions are typically discussed: in terms of right triangles and in terms of the unit circle. The right-angled triangle definition of trigonometric functions is most often how they are ...
The Law of Sines (or Sine Rule) is very useful for solving triangles: a sin A = b sin B = c sin C. It works for any triangle: a, b and c are sides. A, B and C are angles.
The sine function is used to represent sound and light waves in the field of physics. In this article, we will learn the basic properties of sin x, sine graph, its domain and range, derivative, integral, and power series expansion. The sine function is a periodic function and has a period of 2π.
What is sine? In the context of a right triangle, the sine function is simply the ratio of the opposite side to the hypotenuse. For an angle α, the sine function is simply denoted by sin α. In other words, sine is a trigonometric function of any given angle. The following figure 3-1 represents a typical right triangle.
