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Unit circle

Author:Jun Zou

Definition

In mathematics, a unit circle is a circle with a radius of one. 
Being so simple, it is a great way to learn and talk about lengths and angles. The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.
Being so simple, it is a great way to learn and talk about lengths and angles. The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.

Pythagoras

Pythagoras
Pythagoras' Theorem says that for a right angled triangle, the square of the long side equals the sum of the squares of the other two sides: x2 + y2 = 12 Because 12 equals 1, so we have x2 + y2 = 1 (the equation of the unit circle) Also, since x=cos(α) and y=sin(α), we get: cos(α)2 + sin(α)2 = 1

How to calculate sin, cos, tan in a simple way?

How to calculate sin, cos, tan in a simple way?
Draw a triangle with side lengths of 2
Cut the triangle into half. Based on Pythagoras' Theorem, the new side is √3.
Cut the triangle into half. Based on Pythagoras' Theorem, the new side is √3.
Then use sohcahtoa to calcualte sin, cos or tan.
Then use sohcahtoa to calcualte sin, cos or tan.

Remember

Sine is opposite divided by hypotenuse. sin(30°) = opposite/hypotenuse = 1/2 Cosine is the adjacent divided by hypotenuse. cos(30°) = adjacent/hypotenuse = √3/2 Tangent is the opposite divided by adjacent, it also equals to sine divided by cosine. tan(30°) = opposite/adjacent = √3/3

Move the points and find the relationship between angle with sin, cos, tan value

Some useful values you need to remember

Some useful values you need to remember

Questions

What happens when the angle α is 0°?

Check my answer

What happens when the angle α is 90°?

Check my answer

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