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Thought-Process to Discover Knowledge

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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.

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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**.

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think,

figure-out, &

learn.

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

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jogger,

exercise.

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*summary of this topic*

Voice

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Home

Trigonometric Values : Angles in Any Quadrant

» The angle `omega` is measured from positive x-axis

x and y coordinates takes sign

» Trigonometric values can be derived for points `P`, `Q`, and `R`

`sin theta = y`

`cos theta = x`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Trigonometric Ratios can be calculated for any angle between `-oo` and `oo` and the value of ratio can be positive or negative.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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This page explains the quadrants, various angles in different quadrants, trigonometric ratios of such angles.

Starting on learning "Trigonometric Values in Four Quadrants". ;; This page explains the quadrants, various angles in different quadrants, trigonometric ratios of such angles.

What are the quadrants in a 2D coordinate plane?

- 2D coordinate plane is split into four quadrants
- Four Quadrants are numbered as I, II, III, and IV
- both the above

The answer is 'both the above'

What is the meaning of word "quadrant"?

- the word is a name and means nothing.
- Quadrant is derived from one fourth or quarter. It denotes a quarter of the plane.

The answer is 'Quadrant is derived from one fourth or quarter. It denotes a quarter of the plane.'

What is `sin 150^@`?

- `/_150^@` is not possible in right-angled-triangles. So `sin 150^@` is not defined.
- `sin 150^@` can be computed for line on unit circle at `/_150^@`. The projection of the line on x and y axes defines the trigonometric ratios.

The answer is '`sin 150^@` can be computed for line on unit circle at `/_150^@`. The projection of the line on x and y axes defines the trigonometric ratios.'

What is `sin(-30^@)`?

- negative angles are not possible in right-angled-triangles. So `sin(-30^@)` is not defined.
- `sin(-30^@)` can be computed for line of unit circle at `-30^@` angle. The projection of the line on x and y axes defined the trigonometric ratios.

The answer is '`sin(-30^@)` can be computed for line of unit circle at `-30^@` angle. The projection of the line on x and y axes defined the trigonometric ratios.'

Can trigonometric ratios be negative?

- Length of sides of triangles can never be negative. So the trigonometric ratios cannot be negative.
- The projection of line on x and y axes can be positive or negative. So the trigonometric ratios can be positive or negative.

The answer is 'The projection of line on x and y axes can be positive or negative. So the trigonometric ratios can be positive or negative.'

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Understanding Trigonometric Ratios for any Angle: **Consider the line at the given angle in the unit circle. The projections on x and y axes define the trigonometric ratios. The angle can be between `-oo` and `oo` and the projections can be positive or negative.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

What are the quadrants in a 2D coordinate plane?

split;coordinate;plane

2D coordinate plane is split into four quadrants

first;second;third;fourth

Four Quadrants are numbered as first, second, third, and fourth

both;above

both the above

The answer is 'both the above'

What is the meaning of word "quadrant"?

name;nothing

the word is a name and means nothing.

fourth;quarter;derived

Quadrant is derived from one fourth or quarter. It denotes a quarter of the plane.

The answer is 'Quadrant is derived from one fourth or quarter. It denotes a quarter of the plane.'

What is sine 150 degree

right;triangle;not

angle 150 degree is not possible in right-angled-triangles. So sine 150 degree is not defined.

unit;circle;projection

sine 150 degree can be computed for line on unit circle at angle 150 degree. The projection of the line on x and y axes defines the trigonometric ratios.

The answer is 'sine 150 degree can be computed for line on unit circle at angle 150 degree. The projection of the line on x and y axes defines the trigonometric ratios.'

What is sine minus 30 degree?

right;triangle;not

negative angles are not possible in right-angled-triangles. So sine minus 30 is not defined.

unit;circle;projection

sine minus 30 can be computed for line of unit circle at minus 30 degree angle. The projection of the line on x and y axes defined the trigonometric ratios.

The answer is 'sine minus 30 can be computed for line of unit circle at minus 30 degree angle. The projection of the line on x and y axes defined the trigonometric ratios.'

Can trigonometric ratios be negative?

length;triangles;cannot;not;sides

Length of sides of triangles can never be negative. So the trigonometric ratios cannot be negative.

projection;line;axes;positive

The projection of line on x and y axes can be positive or negative. So the trigonometric ratios can be positive or negative.

The answer is 'The projection of line on x and y axes can be positive or negative. So the trigonometric ratios can be positive or negative.'

Trigonometric Ratios can be calculated for any angle between minus infinity and infinity;; and the value of ratio can be positive or negative.

To calculate trigonometric ratios for any angles;; consider the line at the given angle in the unit circle. The projections on x and y axes define the trigonometric ratios. The angle can be between minus infinity and infinity ;; and the projections can be positive or negative.