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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.

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mathsTrigonometryBasics of Trigonometry

### Basics of Angles

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

click on the content to continue..

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

An angle is the measure of rotation between two lines.

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.

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.

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.

An angle is positive if it is measured in counter-clockwise direction.

The figure shows +30^@

An angle is negative if it is measured in clockwise direction.

The figure shows -60^@

The measure of angle /_PQR is -30^@.

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

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

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

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.

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