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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.
mathsAdvanced TrigonometryTrigonometric Values for all angles in unit circle form

### Trigonometric Values in Four Quadrants

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

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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
• 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.
• 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.
• 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.
• 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 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 -oo and oo and the value of ratio can be positive or negative.

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.

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