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summary of this topic

Basics of Trigonometry

Voice

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Home

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.

Keep tapping on the content to continue learning.
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?

• 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 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
• both the above

The answer is 'both the above'.

What is the definition of the measure "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"?

• 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?

• 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?

• 60^@
• -60^@

The answer is '-60^@'

What is the measure of angle /_PQR?

• +30^@
• -30^@

The answer is '-30^@'

What is a "right angle"?

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

The answer is 'both the above'.

What is a "straight angle"?

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

The answer is 'both the above'.

What are "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"?

• 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

Progress

Progress

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
Which of the following is a measure of an angle?
degree
degree
both; above
both the above
What is the definition of the measure "degree"?
1;one;kilometer;km
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 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
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.
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.
both;above
both the above
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