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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.

Read in the blogs more about the unique learning experience at nubtrek.continue
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?trigonometric ratios triangular form hypotenuse

  • `bar(PQ)`
  • `bar(QR)`
  • `bar(PR)`
  • `bar(PR)`

The answer is '`bar(PR)`'

Which side is the opposite side to `/_theta`?trigonometric ratios triangular form opposite side

  • `bar(PQ)`
  • `bar(QR)`
  • `bar(QR)`
  • `bar(PR)`

The answer is '`bar(QR)`'

Which side is the adjacent side to `/_theta`?trigonometric ratios triangular form adjacent side

  • `bar(PQ)`
  • `bar(PQ)`
  • `bar(QR)`
  • `bar(PR)`

The answer is '`bar(PQ)`'

Which side is the opposite side to `/_theta`?trigonometric ratios triangular form opposite side

  • `bar(PQ)`
  • `bar(PQ)`
  • `bar(QR)`
  • `bar(PR)`

The answer is '`bar(PQ)`'

Which side is the adjacent side to `/_theta`?trigonometric ratios triangular form adjacent side

  • `bar(PQ)`
  • `bar(QR)`
  • `bar(QR)`
  • `bar(PR)`

The answer is '`bar(QR)`'

Which side is the hypotenuse?trigonometric ratios triangular form hypotenuse

  • `bar(AB)`
  • `bar(AB)`
  • `bar(BC)`
  • `bar(AC)`

The answer is '`bar(AB)`'

Which side is the hypotenuse?trigonometric ratios triangular form hypotenuse

  • `bar(AB)`
  • `bar(BC)`
  • `bar(AC)`
  • `bar(AC)`

The answer is '`bar(AC)`'

Which side is the opposite side to `/_theta`?trigonometric ratios triangular form opposite side

  • `bar(AB)`
  • `bar(BC)`
  • `bar(AC)`

The answer is '`bar(BC)`'

Which side is the adjacent side to `/_theta`?trigonometric ratios triangular form adjacent side

  • `bar(AB)`
  • `bar(BC)`
  • `bar(BC)`
  • `bar(PR)`

The answer is '`bar(BC)`'

What is `sin theta`?trigonometric ratios triangle form

  • `text(opposite)/text(hypotenuse)`
  • `text(opposite)/text(hypotenuse)`
  • `text(adjacent)/text(hypotenuse)`

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

What is `cos theta`?trigonometric ratios triangle form

  • `text(opposite)/text(hypotenuse)`
  • `text(adjacent)/text(hypotenuse)`
  • `text(adjacent)/text(hypotenuse)`

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

What is `tan theta`?trigonometric ratios triangle form

  • `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`?trigonometric ratios triangle form

  • `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 trigonometric ratios triangle form

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

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

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

What is `1/(cos theta)`?trigonometric ratios triangle form

  • `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`'.trigonometric ratios triangle form

`sec theta`

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

`quad quad = 1/ (cos theta)`

What is `1/(sin theta)`?trigonometric ratios triangle form

  • `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`'.trigonometric ratios triangle form

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

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

`quad quad = 1/ (sin theta)`

What is `1/(tan theta)`?trigonometric ratios triangle form

  • `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`'.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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