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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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mathsTrigonometryBasics of Trigonometry

Basics of Angles

In this page, the basics of Angles required to understand trigonometry is revised.



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Before starting with Trigonometry, let us revise the basics required to understand that.

definition of angle An angle is the measure of rotation between two lines.

angle of a line An angle for a given line in a coordinate system is, the angle from the x-axis to the line, measured in anti-clockwise direction.

An angle is measured in degree or radian.

definition of degree The measure of angle, "degree" is defined by -- Rotation by a full circle is graded into `360` degrees.

From the figure, one should understand.

 •  The angles are measured with respect to the +ve x-axis.

 •  The graded angles are represented for `20^@, 40^@, 60^@, cdots`.

 •  A line making an angle `30^@` is shown.

definition of radian The measure of angle, "radian" is defined by -- `1` radian = angle subtended in a circle, by the arc of length equaling the radius.

From the figure, one should understand

 •  radius of the circle is shown in red dotted line. An arc having length equal to radius of the circle is shown in red dotted arc.

 •  The radian measures `1, 2, 3` radians are marked

 •  The y-axis at `90^@` angle is at `pi/2` radian.

 •  the -ve x-axis at `180^@` angle is at `pi` radian.

 •  the full-circle subtends `2pi` radian or `360^@` angle.

 •  line making `30^@` angle is shown and the angle in radians is `pi/6`.

positive negative angle of a line An angle is positive if it is measured in counter-clockwise direction.

The figure shows `+30^@`

positive negative angle of a line An angle is negative if it is measured in clockwise direction.

The figure shows `-60^@`

angles positive and negative The measure of angle `/_PQR` is `-30^@`.

The angle is measured from `bar(PQ)` to `bar(QR)`, in clockwise direction.

right angle Right angle is angle of measure `90^@` or `pi/2` radian. Note `90^@ = pi/2` radian

straight angle Straight angle is angle of measure `180^@` or `pi` radian.

complementary angles Pair of angles having sum `90^@` are called complementary angles.

The word "complementary" is derived from the word "complete". When one angle completes the right angle with another angle, the angles are called complementary angles.

supplementary angles Pair of angles having sum `180^@` are called Supplementary Angles.

The word "supplement" means "comes as an addition".
In a straight line the pair of supplementary angles come together.

Basics of Angles to learn trigonometry :

 •  Angles measured in degrees and radians.

 •  Right angle and Straight Angle.

 •  Complementary and Supplementary angles.

Angle: For two line segments or rays with common initial point, the amount of rotation in counter clockwise direction from one to another is the angle.

Degree: Rotation by a full circle is graded as `360^@` and angles are measured in that graded scale.

Radian: Rotation by the length of radius along the arc of a circle, is `1` radian. Angles are measured in proportion to the `1` radian measure.

Right Angle: Angle of `90^@` or `pi/2` radian.

Straight Angle: Angle of `180^@` or `pi` radian.

Complementary Angles: Pair of angles having sum `90^@`.

Supplementary Angles: Pair of angles having sum `180^@`.

Solved Exercise Problem:

Which of the following is correct for the two angles `52^@` and `38^@`?

  • Right angle
  • Straight angles
  • Complementary angles
  • Complementary angles
  • Supplementary angles

The answer is 'Complementary angles'

                            
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