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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

Voice

Voice

Home

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`

*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*

trek

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

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` ?

- 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 ` ?

- `PQ`
- `QR`

The answer is 'QR'

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

- `PQ`
- `QR`

The answer is 'QR'

A right angled triangle is shown in figure. 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. 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. 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`'.

*your progress details*

Progress

*About you*

Progress

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"