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summary of this topic

Trigonometric Basic Identities

Trigonometric Basic Identities

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Complementary Angles


 »  Quickly follow that the adjacent and opposite sides swap for complementary angles... no need to memorize.

      `sin(90-theta) = cos theta`
      `cos(90-theta) = sin theta`
      `tan(90-theta) = cot theta`

      `csc(90-theta) = sec theta`
      `sec(90-theta) = csc theta`
      `cot(90-theta) = tan theta`

Trigonometric Ratios for Complementary Angles

plain and simple summary

nub

plain and simple summary

nub

dummy

`sin(90-theta) = cos theta`
`cos(90-theta) = sin theta`

`tan(90-theta) = cot theta`
`cot(90-theta) = tan theta`

`csc(90-theta) = sec theta`
`sec(90-theta) = csc theta`

simple steps to build the foundation

trek

simple steps to build the foundation

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The relationship between trigonometric ratios of an angle and its complementary angle is explained.


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Starting on learning "Trigonometric Ratios for Complementary Angles". ;; The relationship between trigonometric ratios of an angle and its complementary angle is explained.

What is the complementary angle of `theta`?

  • angle that completes `theta` to a right angle
  • `90-theta`
  • both the above

The answer is 'both the above'

In the right angled triangle shown in figure, if `/_P = theta` then what is `/_R` ? angles ratio

  • complementary angle of `theta`
  • `90-theta`
  • both the above

The answer is 'both the above'

In the right angled triangle shown in figure, what is the opposite side for `/_P ` ? angles ratio

  • `PQ`
  • `QR`

The answer is 'QR'

In the right angled triangle shown in figure, what is the adjacent side for `/_R ` ? angles ratio

  • `PQ`
  • `QR`

The answer is 'QR'

A right angled triangle is shown in figure.angles ratio Opposite of `/_theta` = Adjacent of `/_(90-theta)`
Adjacent of `/_theta` = Opposite of `/_(90-theta)`

The trigonometric ratios of `90-theta` can be expressed in terms of trigonometric ratios of `theta` or vice versa. angles ratio complementary angles From the figure
`sin theta = (RQ)/(PR)`
`cos theta = (PQ)/(PR)`
`sin (90-theta) = (PQ)/(PR)`
`cos (90-theta) = (RQ)/(PR)`

Comparing the above, it is concluded that
`sin (90-theta) = cos theta`
`cos (90-theta) = sin theta`

The trigonometric ratios of `90-theta` can be expressed in terms of trigonometric ratios of `theta` or vice versa. angles ratio complementary angles From the figure
`tan theta = (RQ)/(PQ)`
`cot theta = (PQ)/(RQ)`
`tan (90-theta) = (PQ)/(RQ)`
`cot (90-theta) = (RQ)/(PQ)`

Comparing the above, it is concluded that
`tan (90-theta) = cot theta`
`cot (90-theta) = tan theta`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Trigonometric Ratios for Complementary Angles:
`sin(90-theta) = cos theta`
`cos(90-theta) = sin theta`

`tan(90-theta) = cot theta`
`cot(90-theta) = tan theta`

`csc(90-theta) = sec theta`
`sec(90-theta) = csc theta`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Which of the following equals `sin 36`?

  • `cos 54`
  • `tan 54`
  • `sec 54`
  • `sin 54`

The answer is '`cos 54`'

`(tan 75) / (cot 15) = ?`

  • `tan^2 75`
  • `1`

The answer is '`1`' As `cot 15` `=tan(90-15)` `=tan 75`.

Which of the following equals `sin 36 - cos 36 + sin 54`?

  • `sin 54`
  • `sin 36`

The answer is '`sin 36`'.

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What is the complementary angle of theta ?
angle;completes;right
angle that completes theta to a right angle
90;minus
90 minus theta
both;above
both the above
The answer is 'both the above'
In the right angled triangle shown in figure, if angle p equals theta, then what is angle R?
angle;complementary
complementary angle of theta
90;minus
90 minus theta
both;above
both the above
The answer is 'both the above'
In the right angled triangle shown in figure, what is the opposite side for angle p?
p;pee
P Q
r;are;or
Q R
The answer is "Q R"
In the right angled triangle shown in figure, what is the adjacent side for angle r?
p;pee
P Q
r;are;or
Q R
The answer is "Q R"
A right angled triangle is shown in figure. Opposite of angle theta equals adjacent of angle 90 minus theta. ;; Adjacent of angle theta equals opposite of angle 90 minus theta.
The trigonometric ratios of 90 minus theta, can be expressed in terms of trigonometric ratios of theta or vice versa. ;; From the figure, sine theta = R Q by P R ;; cos theta = P Q by P R;; sine 90 minus theta = p Q by P R ;; cos 90-theta
Trigonometric Ratios for Complementary Angles: sine 90 minus theta equals cos theta;; cos 90 minus theta equals sine theta.
Trigonometric ratios of complementary angles are given
The trigonometric ratios of 90 minus theta, can be expressed in terms of trigonometric ratios of theta or vice versa. ;; From the figure, sine theta = R Q by P R ;; cos theta = P Q by P R;; sine 90 minus theta = p Q by P R ;; cos 90-theta
Trigonometric Ratios for Complementary Angles: tan 90 minus theta equals cot theta;; cot 90 minus theta equals tan theta.
Trigonometric ratios of complementary angles are given
Trigonometric Ratios for Complementary Angles: co-secant 90 minus theta equals secant theta;; secant 90 minus theta equals co-secant theta.
Trigonometric ratios of complementary angles are given
Which of the following equals sine 36?
cos
cos 54
tan
tan 54
secant
secant 54
sine
sine 54
The answer is "cos 54"
tan 75 divided by cot 15 equals?
tan
tan squared 75
1
1
The answer is "1". As cot 15 = tan 90 minus 15 = tan 75.
Which of the following equals sine 36 minus cos 36 plus sine 54?
54
sine 54
36
sine 36
The answer is "sin 36"

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