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Algebra and Trigonometry Refresher for Calculus Students

There are three basic functions in trigonometry, each of which is one side of a right-angled triangle divided by another. For more about circles, or a quick refresher, see our page on Circles and Curved Shapes. Conventionally, the centre of the circle is considered as a Cartesian coordinate of 0,0. That is, the x value is 0 and the y value is 0.

Anything to the left of the centre has an x value of less than 0 , or is negative, while anything to the right has a positive value. Similarly anything below the centre point has a y value of less than 0 , or is negative and any point in the top of the circle has a positive y value. Now consider what happens if we draw a radius from the centre of the circle, due east if the circle were a compass.

Introduction to Trigonometry

Marked 1 in the diagram. If we then rotate the radius around the circle in an anticlockwise direction, it will create a series of triangles:. As you rotate the radius around the circle, the other two internal angles and the length of the other two sides all change and therefore affect the value of the sin and cos.

Trigonometry Refresher

You can see that when x i. This represents point 1 , where there is basically no triangle.

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Tangent is quite different. You can also work out the inverse function to sin, cos and tan, which basically means 1 divided by that function.


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This enables you to work out the angle if you have the sin, cos or tan of it. Scientific calculators have sin, cos, and tan functions, as well as inverse functions. Trigonometry also works for other triangles, just not in quite the same way. Instead there are two rules based on a triangle like this:.


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This is a reasonable question, and the answer is at least partly because those who decide the mathematics curriculum in many countries think that you should know about it. However, it does also have a few real-life functions, perhaps the most obvious of which is navigation, especially for boats. Connecter avec:.

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Some rules/guidelines for trigonometry of right triangles

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