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Basics of Trigonometry

Basics of Trigonometry

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Home



Trigonometric Ratios: Triangle form


 »  similar right-triangle

    →  given angle `theta`

    →  position of right-angle with reference to given angle

    →  hypotenuse with reference to the right-angle

    →  position of a side with reference to the given angle : opposite-side

    →  position of another side with reference to the given angle : adjacent-side


 »  Trigonometric Ratios
    →  `sin theta = text(opposite)/text(hypotenuse)`
    →  `cos theta = text(adjacent)/text(hypotenuse)`
    →  `tan theta = text(opposite)/text(adjacent)` `quad = (sin theta)/(cos theta)`


   Note: In advanced trigonometry, a general form "trigonometric values on unit circle" will be introduced.

Triangular Form of Trigonometric Ratios

plain and simple summary

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plain and simple summary

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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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Starting on learning "Triangular Form of trigonometric Ratios". ;; Note: The trigonometric ratios are also called trigonometric values and are defined in unit circle form. This will be explained in advanced trigonometry.

Which side is the hypotenuse?trigonometric ratios triangular form hypotenuse

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

The answer is '`bar(QR)`'

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

  • `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(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(PR)`

The answer is '`bar(QR)`'

Which side is the hypotenuse?trigonometric ratios triangular form hypotenuse

  • `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)`

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(PR)`

The answer is '`bar(BC)`'

What is `sin theta`?trigonometric ratios triangle form

  • `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)`

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

What is `tan theta`?trigonometric ratios triangle form

  • `text(opposite)/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)`
  • `(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)`

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(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)`

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)`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

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Progress

Which side is the hypotenuse?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P R'
Which side is the opposite side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line Q R'
Which side is the adjacent side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P Q'
Which side is the opposite side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P Q'
Which side is the adjacent side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line Q R'
Which side is the hypotenuse?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line A B'
Which side is the hypotenuse?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line A C'
Which side is the opposite side to the angle theta?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line B C'
Which side is the adjacent side to the angle theta?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line B C'
What is sine theta?
opposite
opposite by hypotenuse
adjacent
adjacent by hypotenuse
The answer is 'opposite by hypotenuse'
What is cause theta?
opposite
opposite by hypotenuse
adjacent
adjacent by hypotenuse
The answer is 'adjacent by hypotenuse'
What is tan theta?
opposite by hypotenuse
opposite by hypotenuse
adjacent by hypotenuse
adjacent by hypotenuse
opposite by adjacent
opposite by adjacent
The answer is 'opposite by adjacent'
Which of the following is equivalently tan theta?
one by; sine
one by sine theta
cos;cause;
one by cause theta
sine theta by cause theta;sine by cause; theta by
sine theta by cause theta
The answer is 'sine theta by cause theta'
Revising the definition of trigonometric ratios. ;; sine theta equals opposite side by hypotenuse. ;; cause theta equals adjacent side by hypotenuse. ;; tan theta equals opposite side by adjacent side
What is one by cause theta?
opposite
hypotenuse by opposite
adjacent
hypotenuse by adjacent
The answer is 'hypotenuse by adjacent'
one by cause theta is called as 'secant theta'. ;; secant theta equals hypotenuse by adjacent side. ;; equals one by cause theta
What is one by sine theta?
opposite
hypotenuse by opposite
adjacent
hypotenuse by adjacent
The answer is 'hypotenuse by opposite'
one by sine theta is called as 'co-secant theta'. ;; co-secant theta equals hypotenuse by opposite side. ;; equals one by sine theta
What is one by tan theta?
opposite by adjacent
opposite by adjacent
adjacent by opposite
adjacent by opposite
The answer is 'adjacent by opposite'
one by tan theta is called as 'cot theta'. ;; cot theta equals adjacent side by opposite side. ;; equals one by tan theta
Summary of trigonometric ratios. ;; sine theta equals opposite side by hypotenuse. ;; cause theta equals adjacent side by hypotenuse. ;; tan theta equals opposite side by adjacent side. ;; secant theta equals hypotenuse by adjacent side. ;; co-secant theta equals hypotenuse by opposite side. ;; cot theta equals adjacent side by opposite side

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