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Thought-Process to Discover Knowledge

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User Guide

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summary of this topic

### Trigonometric Values for all angles in unit circle form

Voice

Voice

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

### Trigonometric Values in Four Quadrants

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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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

Progress

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.

we are not perfect yet...