Special Angle

In Trigonometry there are special angle, there are 5 special angle: 0 °, 30 °, 45 °, 60 ° and 90 °. Known special angle for the value of the trigonometric functions of these numbers can be obtained through a simple calculation.

We start from an angle of 45 °.

Starting from a square unit (long side is 1 unit) ABCD. We get a right-angled triangle ABC, with right-angled in C and by using Pythagoras' argument we obtain the length of the hypotenuse is √2. Easily we know a great angle A is 45 °.

$\sin45^{\circ}=\frac{1}{\sqrt{2}}=\frac{1}{2}\sqrt{2}$
$\cos45^{\circ}=\frac{1}{\sqrt{2}}=\frac{1}{2}\sqrt{2}$
$\tan45^{\circ}=\frac{1}{1}=1$

Furthermore angle of 30 ° and 60 °

Starting from the equilateral triangle side length is 2 units, whose name is large equilateral triangle each angle is 60 °. Kemudain we cut in the high line, so that we get a right-angled triangle large non elbow angles are 30 ° and 60 °. By using the argument of Pythagoras, the length of the line height is √3.

$\sin60^{\circ}=\frac{\sqrt{3}}{2}$
$\cos60^{\circ}=\frac{1}{2}$
$\tan60^{\circ}=\frac{\sqrt{3}}{1}=\sqrt{3}$

While 30 °

$\sin30^{\circ}=\frac{1}{2}$
$\cos30^{\circ}=\frac{\sqrt{3}}{2}$
$\tan30^{\circ}=\frac{1}{\sqrt{3}}=\frac{1}{3}\sqrt{3}$

Angle of 0 ° and 90 °

Suppose α is the angle between the hypotenuse with the pedestal. What happens if α = 0 °? Which happened right oblique side will coincide / attached to the side of the pedestal. In other words, the hypotenuse = the board, let alone the length of a unit. That means the front side length is zero.

$\sin0^{\circ}=\frac{0}{a}=0$
$\cos0^{\circ}=\frac{a}{a}=1$
$\tan0^{\circ}=\frac{0}{a}=0$

Furthermore, what would happen if α = 90 °? Which happened right oblique side will coincide / attached to the front side. In other words, the hypotenuse = front side. That means the base length is zero.