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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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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.

In the given figure, bar(PR) is the hypotenuse.

In the given figure, bar(QR) is the opposite side.

In the given figure, bar(PQ) is the adjacent side.

In the given figure, the opposite side to /_theta is bar(PQ).

In the given figure, the adjacent side to /_theta is bar(QR).

In the given figure, the hypotenuse is bar(AB).

In the given figure, the hypotenuse is bar(AC).

In the given figure, the opposite side to /_theta is bar(BC).

In the given figure, the adjacent side to /_theta is bar(BC).

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

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

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

tan theta = (sin theta)/(cos theta)

Revising the definition of trigonometric ratios

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

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

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

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

1/(cos theta) is called as 'sec theta'.

sec theta

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

quad quad = 1/ (cos theta)

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

1/(sin theta) is called as 'text(cosec) theta' or 'csc theta'.

text(cosec) theta or csc theta

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

quad quad = 1/ (sin theta)

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

1/(tan theta) is called as 'cot theta'.

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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