Trigonometric Ratios of 0°, 180°, 270° and 360°

Trigonometric Ratios of 0° 

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,

$\displaystyle \sin 360°=y=0$

$\displaystyle \cos 360°=x=1$

$\displaystyle \tan 360°=\frac{y}{x}=\frac{0}{1}=1$

$\displaystyle \cot 360°=\frac{x}{y}=\frac{1}{0}=\text{undefined}$

$\displaystyle \sec 360°=\frac{1}{x}=\frac{1}{1}=1$

$\displaystyle \operatorname{cosec} 360°=\frac{1}{y}=\frac{1}{0}=\text{undefined}$


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