Trigonometric Ratios of Complementary Angles

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Name

Trigonometric ratios of Complementary Angles
Figure Let
\triangle AOH:\,


O=\text{ side adjacent to angle }\theta\,

A=\text{ side opposite to angle }\theta\,

H=\text{ hypotenuse}\,

\delta=90-\theta\,


Trigonometrical

ratio of angle

\theta\;
Trigonometrical

ratio of complementary angle

\delta=90-\theta\;
Formulas
\sin \theta=\frac{O}{H} \cos \delta=\frac{O}{H} \sin \theta=\cos \delta\, \sin \theta=\cos (90-\theta)\,
\cos \theta=\frac{A}{H} \sin \delta=\frac{A}{H} \cos \theta=\sin \delta\, \cos \theta=\sin (90-\theta)\,
\tan \theta=\frac{O}{A} \cot \delta=\frac{O}{A} \tan \theta=\cot \delta\, \tan \theta=\cot (90-\theta)\,
\cot \theta=\frac{A}{O} \tan \delta=\frac{A}{O} \cot \theta=\tan \delta\, \cot \theta=\tan (90-\theta)\,
\sec \theta=\frac{H}{A} \csc \delta=\frac{H}{A} \sec \theta=\csc \delta\, \sec \theta=\csc (90-\theta)\,
\csc \theta=\frac{H}{O} \sec \delta=\frac{H}{O} \csc \theta=\sec \delta\, \csc \theta=\sec (90-\theta)\,



Usage


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