__maths__>__Advanced Trigonometry__>__Trigonometric 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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