The 5 special Triangles - Daily Math Guide

The 5 special Triangles - Daily Math Guide

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The 5 special Triangles

Posted by : Allan_Dell on Sunday, April 26, 2020 | 11:40 PM

The Five special Triangles

The ${\color{Red} 30^{0}}-{\color{Blue}60^{0}}-90^{0}$ .

The five special triangles has their angles permanent values. They are, 30-60-90, 45-45-90, 0, and 90 degrees. These five triangles are very useful when we are solving right triangles with only one side or angle is given. Proportion is the key. Below were the said triangles with their corresponding trigonometric functions.

The six trigonometric function of $\angle {\color{Red} 30^{0}}$ .

$sin{\color{Red} 30^{0}}=\frac{1}{2}$ $cotan{\color{Red} 30^{0}}=\frac{\sqrt{3}}{1}=\sqrt{3}$

$cosin{\color{Red} 30^{0}}={\frac{\sqrt{3}}{2}}$ $sec{\color{Red} 30^{0}}=\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$

$tan{\color{Red} 30^{0}}={\frac{{1}}{\sqrt{3}}}.\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}$ $csc{\color{Red} 30^{0}}=\frac{2}{1}=2$

The six trigonometric function of $\angle {\color{Blue} 60^{0}}$ .

$sin{\color{Blue} 60^{0}}=\frac{\sqrt{3}}{2}$ $cot{\color{Blue} 60^{0}}=\frac{1}{\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{{3}}$

$cos{\color{Blue} 60^{0}}=\frac{1}{2}$ $sec{\color{Blue} 60^{0}}=\frac{2}{1}=2$

$tan{\color{Blue} 60^{0}}=\frac{\sqrt{3}}{1}=\sqrt{3}$ $csc{\color{Blue} 60^{0}}=\frac{2}{\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{{3}}$

The ${45^{0}}-{45^{0}}-90^{0}$ . This is an isosceles triangle.

The six trigonometric function of $\angle 45^{0}$ .

$sin45^{0}=\frac{1}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{{2}}$ $cot45^{0}=\frac{1}{1}=1$

$cos45^{0}=\frac{1}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$ $sec45^{0}=\frac{\sqrt{2}}{1}=\sqrt{2}$

$tan45^{0}=\frac{1}{1}=1$ $csc45^{0}=\frac{\sqrt{2}}{1}=\sqrt{2}$

The $90^{0}$ .

The six trigonometric function of $90^{0}$ .

$sin90^{0}=\frac{1}{1}=1$ $cot90^{0}=\frac{0}{1}=0$

$cos90^{0}=\frac{0}{1}=0$ $sec0^{0}=\frac{1}{0}=undefined$

$tan90^{0}=\frac{1}{0}=undefined$ $csc0^{0}=\frac{1}{1}=1$

The $0^{0}$ .

The six trigonometric function of $0^{0}$ .

$sin0^{0}=\frac{0}{1}=0$ $cot0^{0}=\frac{1}{0}=undefined$

$cos0^{0}=\frac{1}{1}=1$ $sec0^{0}=\frac{1}{1}=1$

$tan0^{0}=\frac{0}{1}=0$ $csc0^{0}=\frac{1}{0}=undefined$

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