Server Not Reachable. *This may be due to your internet connection or the nubtrek server is offline.*

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

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. *

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

*To stop this message from appearing, please choose an option and make a payment.*

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.

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?

- `bar(PQ)`
- `bar(QR)`
- `bar(PR)`

The answer is '`bar(PR)`'

Which side is the opposite side to `/_theta`?

- `bar(PQ)`
- `bar(QR)`
- `bar(PR)`

The answer is '`bar(QR)`'

Which side is the adjacent side to `/_theta`?

- `bar(PQ)`
- `bar(QR)`
- `bar(PR)`

The answer is '`bar(PQ)`'

Which side is the opposite side to `/_theta`?

- `bar(PQ)`
- `bar(QR)`
- `bar(PR)`

The answer is '`bar(PQ)`'

Which side is the adjacent side to `/_theta`?

- `bar(PQ)`
- `bar(QR)`
- `bar(PR)`

The answer is '`bar(QR)`'

Which side is the hypotenuse?

- `bar(AB)`
- `bar(BC)`
- `bar(AC)`

The answer is '`bar(AB)`'

Which side is the hypotenuse?

- `bar(AB)`
- `bar(BC)`
- `bar(AC)`

The answer is '`bar(AC)`'

Which side is the opposite side to `/_theta`?

- `bar(AB)`
- `bar(BC)`
- `bar(AC)`

The answer is '`bar(BC)`'

Which side is the adjacent side to `/_theta`?

- `bar(AB)`
- `bar(BC)`
- `bar(PR)`

The answer is '`bar(BC)`'

What is `sin theta`?

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

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

What is `cos theta`?

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

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

What is `tan theta`?

- `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`?

- `1/ (sin theta)`
- `1/(cos theta)`
- `(sin theta)/(cos theta)`

The answer is '`(sin theta)/(cos theta)`'

Revising the definition of trigonometric ratios

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

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

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

What is `1/(cos theta)`?

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

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

`1/(cos theta)` is called as '`sec theta`'.

`sec theta`

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

`quad quad = 1/ (cos theta)`

What is `1/(sin theta)`?

- `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`'.

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

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

`quad quad = 1/ (sin theta)`

What is `1/(tan theta)`?

- `text(opposite)/text(adjacent)`
- `text(adjacent)/text(opposite)`

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

`1/(tan theta)` is called as '`cot theta`'.

`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

*About you*

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