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Thought-Process to Discover Knowledge

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mathsTrigonometryBasics of Trigonometry

Triangular Form of Trigonometric Ratios

In this page, the trigonometric ratios defined in triangular form is revised.

Note: The trigonometric ratios are also called trigonometric values and are defined in unit circle form. This will be explained in advanced trigonometry.



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Let us quickly review the terminology in trigonometric ratios.

trigonometric ratios triangular form hypotenuse In the given figure, `bar(PR)` is the hypotenuse.

trigonometric ratios triangular form opposite side In the given figure, `bar(QR)` is the opposite side.

trigonometric ratios triangular form adjacent side In the given figure, `bar(PQ)` is the adjacent side.

trigonometric ratios triangular form opposite side In the given figure, the opposite side to `/_theta` is `bar(PQ)`.

trigonometric ratios triangular form adjacent side In the given figure, the adjacent side to `/_theta` is `bar(QR)`.

trigonometric ratios triangular form hypotenuse In the given figure, the hypotenuse is `bar(AB)`.

trigonometric ratios triangular form hypotenuse In the given figure, the hypotenuse is `bar(AC)`.

trigonometric ratios triangular form opposite side In the given figure, the opposite side to `/_theta` is `bar(BC)`.

trigonometric ratios triangular form adjacent side In the given figure, the adjacent side to `/_theta` is `bar(BC)`.

trigonometric ratios triangle form `sin theta = text(opposite)/text(hypotenuse)`

trigonometric ratios triangle form `cos theta = text(adjacent)/text(hypotenuse)`

trigonometric ratios triangle form `tan theta = text(opposite)/text(adjacent)`

trigonometric ratios triangle form `tan theta = (sin theta)/(cos theta)`

Revising the definition of trigonometric ratios trigonometric ratios triangle form

`sin theta = text(opposite)/text(hypotenuse)`

`cos theta = text(adjacent)/text(hypotenuse)`

`tan theta = text(opposite)/text(adjacent)`

trigonometric ratios triangle form `1/(cos theta) = text(hypotenuse)/text(adjacent)`

`1/(cos theta)` is called as '`sec theta`'.trigonometric ratios triangle form

`sec theta`

`quad quad = text(hypotenuse)/text(adjacent)`

`quad quad = 1/ (cos theta)`

trigonometric ratios triangle form `1/(sin theta) = text(hypotenuse)/text(opposite)`

`1/(sin theta)` is called as '`text(cosec) theta`' or '`csc theta`'.trigonometric ratios triangle form

`text(cosec) theta` or `csc theta`

`quad quad = text(hypotenuse)/text(opposite)`

`quad quad = 1/ (sin theta)`

trigonometric ratios triangle form `1/(tan theta) = text(adjacent)/text(opposite)`

`1/(tan theta)` is called as '`cot theta`'.trigonometric ratios triangle form

`text(tan) theta`

`quad quad = text(adjacent)/text(opposite)`

`quad quad = 1/ (tan theta)`

Trigonometric Ratios:
`sin theta = text(opposite)/text(hypotenuse)`

`cos theta = text(adjacent)/text(hypotenuse)`

`tan theta = text(opposite)/text(adjacent)`

`sec theta = text(hypotenuse)/text(adjacent)`

`text(cosec) theta = text(hypotenuse)/text(opposite)`

`cot theta = text(adjacent)/text(opposite)`

                            
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