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summary of this topic

Basics of Trigonometry

Basics of Trigonometry

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Revising Angles


 »  Angle is measured in degree or radian

 »  Right Angle : `90^@`

 »  Complementary Angles : pair of angles with sum `90^@`

 »  Straight Angle : `180^@`

 »  Supplementary Angles : pair of angles with sum `180^@`

Basics of Angles

plain and simple summary

nub

plain and simple summary

nub

dummy

Basics of Angles to learn trigonometry :

 •  Angles measured in degrees and radians.

 •  Right angle and Straight Angle.

 •  Complementary and Supplementary angles.

simple steps to build the foundation

trek

simple steps to build the foundation

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


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Starting on learning "Basics of Angles". ;; In this page, the basics of Angles required to understand trigonometry is revised.

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

What is an angle?definition of angle

  • measure of rotation between two lines
  • length of a line

The answer is 'measure of rotation between two lines'

What is an angle for a given line in a coordinate system?angle of a line

  • angle is not defined for a single line
  • the angle from the x-axis to the line
  • the angle from the y-axis to the line

The answer is 'the angle from the x-axis to the line'

Which of the following is a measure of an angle?

  • degree
  • radian
  • both the above

The answer is 'both the above'.

What is the definition of the measure "degree"?definition of degree

  • `1000` km = `1` degree
  • Rotation by a full circle is graded into `360` degrees

The answer is '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.

What is the definition of the measure "radian"?definition of radian

  • `1` radian = `1` degree
  • `1` radian = `10` degree
  • `1` radian = angle subtended by the arc of length equaling radius

The answer is '`1` radian = angle subtended by the arc of length equaling radius'.

From the figure, one should understand

 •  radius of the circle and the arc having length equal to radius of the circle are shown in red dotted line and 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`.

Given the magnitude of angle between x-axis and line `bar(OP)` is `30^@`, what is the given angle?positive negative angle of a line

  • `30^@`
  • `-30^@`

The answer is '`+30^@`'

Given the magnitude of angle between x-axis and line `bar(OQ)` is `60^@`, what is the given angle?positive negative angle of a line

  • `60^@`
  • `-60^@`

The answer is '`-60^@`'

What is the measure of angle `/_PQR`?angles positive and negative

  • `+30^@`
  • `-30^@`

The answer is '`-30^@`'

What is a "right angle"?right angle

  • Angle at `90^@`
  • Angle at `pi/2` radian
  • both the above

The answer is 'both the above'.

What is a "straight angle"?straight angle

  • Angle at `180^@`
  • Angle at `pi` radian
  • both the above

The answer is 'both the above'.

What are "Complementary Angles"?complementary angles

  • Pair of angles having sum `90^@`
  • One angle that completes right angle with another angle
  • both the above

The answer is 'Both the Above'

What are "Supplementary Angles"?supplementary angles

  • Pair of angles having sum `180^@`
  • One angle that supplements(comes as an addition) with another angle in a straight angle
  • both the above

The answer is 'Both the Above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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^@`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

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

The answer is 'Complementary angles'

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Before starting with Trigonometry, let us revise the basics required to understand that.
What is an angle?
rotation; between
measure of rotation between two lines
length
length of a line
The answer is 'measure of rotation between two lines'
What is an angle for a given line in a coordinate system?
not defined; single
angle is not defined for a single line
x axis; x-axis
the angle from the x-axis to the line
y axis; y-axis
the angle from the y-axis to the line
The answer is ""
Which of the following is a measure of an angle?
degree
degree
radian
radian
both; above
both the above
The answer is both degree and radian.
What is the definition of the measure "degree"?
1;one;kilometer;km
1000 km = 1 degree
rotation;full circle;graded;360
Rotation by a full circle is graded into 360 degrees
The answer is Rotation by a full circle is graded into 360 degrees. ;; From the figure, one should understand;; The angles are measured with respect to the positive x-axis.;; The graded angles are represented for 20 degree, 40 degree, 60 degree et cetera. ;; A line making an angle 30 degree is shown
What is the definition of the measure "radian"?
1 degree
1 radian = 1 degree
10 degree
1 radian = 10 degree
subtended;arc of length
1 radian = angle subtended by the arc of length equaling radius
The answer is ' 1 radian = angle subtended by the arc of length equaling 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 dottrf arc. ;; The radian measures 1, 2, and 3 are marked. ;; The y-axis at 90 degree angle is at pi by 2 radian. ;; the negative x-axis at 180 degree angle is at pi radian. ;; the full-circle subtends 2 pi radian or 360 degree angle. ;; line making 30 degree angle is shown and the angle in radians is pi by 6
Given the magnitude of angle between x-axis and line O P is 30 degree , what is the given angle?
plus
+ 30 degree
minus
-30 degree
The answer is plus 30 degree
Given the magnitude of angle between x-axis and line O Q is 60 degree , what is the given angle?
plus
+ 60 degree
minus
-60 degree
The answer is minus 60 degree. The angles are measured in counter-clockwise direction. When a given angle is measured in clockwise direction, it is negative.
What is the measure of angle P Q R ?
plus
plus 30 degree
minus
minus 30 degree
The answer is minus 30 degree. The angle is measured from line P Q to line Q R, in clockwise direction.
What is a "right angle"?
degree
angle at 90 degree.
radian
angle at pi by 2 radian.
both;above
both the above
The answer is 'both the above'. 90 degree equals pi by 2 radian.
What is a "straight angle"?
180;degree
angle at 180 degree.
pi;radian
angle at pi radian.
both;above
both the above
The answer is both the above. 180 degree equals pi radian.
What are "Complementary Angles"?
sum; degree; 90; ninety
Pair of angles having sum 90 degree
complete;right angle
One angle that completes right angle with another angle
both;above
both the above
The answer is 'Both the Above'. The word "complementary" is derived from the word "complete". When one angle completes the right angle with another angle, the angles are called complementary angle.
What are "Supplementary Angles"?
sum; 180; degree
Pair of angles having sum 180 degree.
supplement;another angle; straight
One angle that supplements with another angle in a straight angle.
both;above
both the above
The answer is 'Both the Above'. The word "supplement" means "comes as an addition".
The following basics of angles are required to learn trigonometry.; angles measured in degrees and radians. ; Right angle and Straight Angle. ; Complementary and Supplementary angles. ;
The reference material is given for you to revise anytime.
Which of the following is correct for the two angles 52 degree and 38 degree ?
right
Right angle
straight
Straight angles
complementary
Complementary angles
supplementary
Supplementary angles
The answer is 'Complementary angles'

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