From the unit circle we have ,
$ \displaystyle \sin 0°=y=0$
$ \displaystyle \cos 0°=x=1$
Therefore
$ \displaystyle \tan 0°=\frac{y}{x}=\frac{0}{1}=1$
$ \displaystyle \cot 0°=\frac{x}{y}=\frac{1}{0}=\text{undefined}$
$ \displaystyle \sec 0°=\frac{1}{x}=\frac{1}{1}=1$
$ \displaystyle \operatorname{cosec} 0°=\frac{1}{y}=\frac{1}{0}=\text{undefined}$
Trigonometric Ratios of 90°
Similarly,
$ \displaystyle \sin 90°=y=1$
$ \displaystyle \cos 90°=x=0$
$ \displaystyle \tan 90°=\frac{y}{x}=\frac{1}{0}=\text{undefined}$
$ \displaystyle \cot 90°=\frac{x}{y}=\frac{0}{1}=0$
$ \displaystyle \sec 90°=\frac{1}{x}=\frac{1}{0}=\text{undefined}$
$ \displaystyle \operatorname{cosec} 90°=\frac{1}{y}=\frac{1}{1}=1$
Trigonometric Ratios of 180°
Similarly,
$ \displaystyle \sin 180°=y=0$
$ \displaystyle \cos 180°=x=-1$
$ \displaystyle \tan 180°=\frac{y}{x}=\frac{0}{-1}=0$
$ \displaystyle \cot 180°=\frac{x}{y}=\frac{-1}{0}=\text{undefined}$
$ \displaystyle \sec 180°=\frac{1}{x}=\frac{1}{-1}=-1$
$ \displaystyle \operatorname{cosec} 180°=\frac{1}{y}=\frac{1}{0}=\text{undefined}$
Trigonometric Ratios of 270°
Similarly,
$ \displaystyle \sin 270°=y=-1$
$ \displaystyle \cos 270°=x=0$
$ \displaystyle \tan 270°=\frac{y}{x}=\frac{-1}{0}=\text{undefined}$
$ \displaystyle \cot 270°=\frac{x}{y}=\frac{0}{-1}=0$
$ \displaystyle \sec 270°=\frac{1}{x}=\frac{1}{0}=\text{undefined}$
$ \displaystyle \operatorname{cosec} 270°=\frac{1}{y}=\frac{1}{-1}=-1$
Trigonometric Ratios of 360°
Similarly,
$ \displaystyle \sin 360°=y=0$
$ \displaystyle \cos 360°=x=1$
$ \displaystyle \tan 360°=\frac{y}{x}=\frac{0}{1}=1$
$ \displaystyle \cot 360°=\frac{x}{y}=\frac{1}{0}=\text{undefined}$
$ \displaystyle \sec 360°=\frac{1}{x}=\frac{1}{1}=1$
$ \displaystyle \operatorname{cosec} 360°=\frac{1}{y}=\frac{1}{0}=\text{undefined}$
Applet တြင္ undefined အတြက္ ∞ သေကၤတ ကို သံုးထားပါသည္။
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