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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.

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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.

Which side is the hypotenuse? • bar(PQ)
• bar(QR)
• bar(PR)
• bar(PR)

The answer is 'bar(PR)'

Which side is the opposite side to /_theta? • bar(PQ)
• bar(QR)
• bar(QR)
• bar(PR)

The answer is 'bar(QR)'

Which side is the adjacent side to /_theta? • bar(PQ)
• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(PQ)'

Which side is the opposite side to /_theta? • bar(PQ)
• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(PQ)'

Which side is the adjacent side to /_theta? • bar(PQ)
• bar(QR)
• bar(QR)
• bar(PR)

The answer is 'bar(QR)'

Which side is the hypotenuse? • bar(AB)
• bar(AB)
• bar(BC)
• bar(AC)

The answer is 'bar(AB)'

Which side is the hypotenuse? • bar(AB)
• bar(BC)
• bar(AC)
• bar(AC)

The answer is 'bar(AC)'

Which side is the opposite side to /_theta? • bar(AB)
• bar(BC)
• bar(AC)

The answer is 'bar(BC)'

Which side is the adjacent side to /_theta? • bar(AB)
• bar(BC)
• bar(BC)
• bar(PR)

The answer is 'bar(BC)'

What is sin theta? • text(opposite)/text(hypotenuse)
• text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)

The answer is 'text(opposite)/text(hypotenuse)'

What is cos theta? • text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)

The answer is 'text(adjacent)/text(hypotenuse)'

What is tan theta? • text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)
• text(opposite)/text(adjacent)

The answer is 'text(opposite)/text(adjacent)'

Which of the following is equivalently tan theta? • 1/ (sin theta)
• 1/(cos theta)
• 1/(cos theta)
• (sin theta)/(cos theta)

The answer is '(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)

What is 1/(cos theta)? • text(hypotenuse)/text(opposite)
• text(hypotenuse)/text(adjacent)
• text(hypotenuse)/text(adjacent)

The answer is '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)

What is 1/(sin theta)? • text(hypotenuse)/text(opposite)
• text(hypotenuse)/text(opposite)
• text(hypotenuse)/text(adjacent)

The answer is '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)

What is 1/(tan theta)? • text(opposite)/text(adjacent)
• text(adjacent)/text(opposite)
• text(adjacent)/text(opposite)

The answer is '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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