Being so simple, it is a great way to learn and talk about lengths and angles.[br]The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.
Unit circle
Definition
[color=#252525]In mathematics, a unit circle is a circle with a radius of one. [/color]
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:[br][color=#1155cc]x[sup]2[/sup] + y[sup]2[/sup] = 1[/color][sup][color=#1155cc]2[/color][br][/sup]Because 1[sup]2[/sup] equals 1, so we have[br][color=#1155cc]x[sup]2[/sup] + y[sup]2 [/sup]= 1 [/color] (the equation of the unit circle)[br]Also, since x=cos(α) and y=sin(α), we get:[br][color=#1155cc]cos(α)[sup]2[/sup] + sin(α)[sup]2[/sup] = 1 [/color]
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.
Then use sohcahtoa to calcualte sin, cos or tan.
Remember
Sine is opposite divided by hypotenuse.[br][color=#1155cc]sin(30°) = opposite/hypotenuse = 1/2[/color][br]Cosine is the adjacent divided by hypotenuse.[br][color=#1155cc]cos(30°) = adjacent/hypotenuse = √3/2[/color][br]Tangent is the opposite divided by adjacent, it also equals to sine divided by cosine.[br][color=#1155cc]tan(30°) = opposite/adjacent = √3/3[/color]
Move the points and find the relationship between angle with sin, cos, tan value
Some useful values you need to remember
Questions
What happens when the angle α is 0°?
What happens when the angle α is 90°?