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Trigonometric Basic Identities

Trigonometric Basic Identities

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Pythagorean Trigonometric Identities


 »  `text(opposite)^2``+text(adjacent)^2`` = text(hypotenuse)^2`


 »  Divide the above by `text(hypotenuse)^2`
      `sin^2 theta + cos^2 theta = 1`


 »  Divide the identity by `cos^2 theta`
      `tan^2 theta + 1 = sec^2 theta`


 »  Divide the identiry by `sin^2 theta`
      `1 + cos^2 theta = csc^2 theta`

Pythagorean Trigonometric Identities

plain and simple summary

nub

plain and simple summary

nub

dummy

`sin^2 theta + cos^2 theta = 1` for any `theta`.

`1 + cot^2 theta = csc^2 theta` for any `theta`.

`tan^2 theta + 1 = sec^2 theta` for any `theta`.

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simple steps to build the foundation

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The relationship between trigonometric ratios per Pythagorean theorem is explained and referred as "Pythagorean Trigonometric Identities"


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Starting on learning "Pythagorean Trigonometric Identities". ;; The relationship between trigonometric ratios per Pythagorean theorem is explained and referred as "Pythagorean Trigonometric Identities"

For the triangle given in figure, What is `sin theta`?Pythagorean Trigonometric Identities illustration

  • `(OP)/(OQ)`
  • `(PQ)/(OQ)`

The answer is '`(PQ)/(OQ)`'

For the triangle given in figure, What is `cos theta`?Pythagorean Trigonometric Identities illustration

  • `(OP)/(OQ)`
  • `(PQ)/(OQ)`

The answer is '`(OP)/(OQ)`'

For the triangle given in figure, which of the following represents Pythagoras theorem?Pythagorean Trigonometric Identities illustration

  • `OP^2 + PQ^2 =OQ^2`
  • `((OP)/(OQ))^2 + ((PQ)/(OQ))^2 = 1`
  • Both the above

The answer is 'both the above'.

For a right angled triangle, the Pythagoras theorem is given as

`(text(opposite))^2` `+ (text(adjacent))^2` `= (text(hypotenuse))^2`

If this equation is divided by `(text(hypotenuse))^2` ; which of the following is the result?

  • `((OP)/(OQ))^2 + ((PQ)/(OQ))^2 = 1`
  • `sin^2 theta + cos^2 theta = 1`
  • Both the above

The answer is 'both the above'.

Pythagorean Theorem states that in a right angled triangle, square of hypotenuse equals sum of squares of two arms. The trigonometric ratios are defined for right angled triangles. The relationships between trigonometric ratios per Pythagorean theorem are called "Pythagorean Trigonometric Identities".

What does 'identity' mean?

  • It is just a name.
  • equality of two expressions; left and right hand side are identical

Answer is 'equality of two expressions; left and right hand side are identical'

For a right angled triangle,

`sin^2 theta + cos^2 theta = 1`

If this equation is divided by `sin^2 theta` ; which of the following is the result?Pythagorean Trigonometric Identities illustration

  • cannot divide this equation by `sin^2 theta`
  • `1+cot^2 theta = csc^2 theta`

The answer is '`1+cot^2 theta = csc^2 theta`'.

For a right angled triangle,

`sin^2 theta + cos^2 theta = 1`

If this equation is divided by `cos^2 theta` ; which of the following is the result?Pythagorean Trigonometric Identities illustration

  • cannot divide this equation by `cos^2 theta`
  • `tan^2 theta + 1 = sec^2 theta`

The answer is '`tan^2 theta + 1 = sec^2 theta`'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Pythagorean Trigonometric Identities:

`sin^2 theta + cos^2 theta = 1`

`1+cot^2 theta = csc^2 theta`

`tan^2 theta + 1 = sec^2 theta`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is the value of `1-sin^2 theta`?

  • `cos^2 theta`
  • the question is incomplete to find an answer

The answer is '`cos^2 theta`'.

This is derived from the Pythagorean trigonometric identity `sin^2 theta + cos^2 theta = 1`

What is the value of `sec^2 theta - 1`?

  • `tan^2 theta`
  • `cot^2 theta`

The answer is '`tan^2 theta`'.

This is derived from the Pythagorean trigonometric identity `tan^2 theta + 1 = sec^2 theta`

What is the value of `csc^2 theta-cot^2 theta`?

  • `cos^2 theta`
  • 1

The answer is '`1`'.

This is derived from the Pythagorean trigonometric identity `1 + cot^2 theta = csc^2 theta`

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For the triangle given in figure, What is sine theta?
oh;O;o;oh pee
O P by O Q
pee queue;PQ
P Q by O Q
The answer is P Q by O Q
For the triangle given in figure, What is cos theta?
oh;O;o;oh pee
O P by O Q
pee queue;PQ
P Q by O Q
The answer is O P by O Q
For the triangle given in figure, which of the following represents Pythagoras theorem?
OP squared;PQ squared
O P squared plus P Q squared equals O Q squared
one;equal one;1;equal 1;by;buy
O P by O Q squared plus p q by O Q squared equal 1
both;above
Both the above
The answer is 'both the above'.
For a right angled triangle, the Pythagoras theorem is given as, opposite squared, plus adjacent squared, equals hypotenuse squared. If this equation is divided by hypotenuse squared, which of the following is the result?
one;equal one;1;equal 1;by;buy
O P by O Q squared plus p q by O Q squared equal 1
sine;cos;theta
sine squared theta plus cos squared theta equals 1
both;above
Both the above
The answer is 'both the above'.
Pythagorean Theorem states that in a right angled triangle, square of hypotenuse equals sum of squares of two arms. The trigonometric ratios are defined for right angled triangles. The relationships between trigonometric ratios per Pythagorean theorem are called "Pythagorean Trigonometric Identities".
First Pythagorean trigonometric Identity : sine squared theta plus cos squared theta equals 1, for any theta
Pythagorean Trigonometric Identities: For any theta, sine squared theta plus cos squared theta equals 1
What does 'identity' mean?
just;name
It is just a name.
equality;2;expressions;left;right
equality of two expressions; left and right hand side are identical
Answer is 'equality of two expressions; left and right hand side are identical'
For a right angled triangle, sine squared theta, + cos squared theta = 1. If this equation is divided by sine squared theta, which of the following is the result?
cannot;divide;equation
cannot divide this equation by sine squared theta
1;plus;cot;equals;
1 plus cot squared theta = co-secant squared theta
The answer is 1 plus cot squared theta = co-secant squared theta
Another Pythagorean Trigonometric Identity is ; 1 plus cot squared theta equals co-secant squared theta; for any theta.
1 plus cot squared theta = co-secant squared theta
For a right angled triangle, sine squared theta, + cos squared theta = 1. If this equation is divided by cos squared theta, which of the following is the result?
cannot;divide;equation
cannot divide this equation by cos squared theta
1;plus;tan;equals;
tan squared theta plus 1 = secant squared theta
The answer is tan squared theta plus 1 = secant squared theta
Another Pythagorean Trigonometric Identity is ; tan squared theta plus 1 = secant squared theta; for any theta.
tan squared theta plus 1 = secant squared theta
What is the value of 1 minus sine squared theta?
cos;squared;theta
cos squared theta
question;incomplete;find;answer
the question is incomplete to find an answer
The answer is "cos squared theta"
What is the value of secant squared theta minus 1?
tan
tan squared theta
cot
cot squared theta
The answer is "tan squared theta"
What is the value of co-secant squared theta minus cot squared theta?
cos;squared;theta
cos squared theta
1
1
The answer is "1"

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