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Chapter no 7
Introduction to Trigonometry
10th Class Mathematics Science Group, Exercise 7.3 Question no 7, 8, 9, 10

Trigonometry:
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The name trigonometry comes from Greek trigonon "triangle" + metron "measure".

Angle:
In geometry, an angle can be defined as the figure formed by two non-collinear rays meeting at a common end point.
An angle is represented by the symbol ∠.
Angles are measured in degrees, using a protractor.

Arms: The two rays joining to form an angle are called arms of an angle.
Vertex: The common end point at which the two rays meet to form an angle is called the vertex.

Sexagesimal System:
In Sexagesimal System, an angle is measured in degrees, minutes and seconds.

Degree:
we divide the circumference of a circle into 360 equal arcs. The angle subtended at the centre of the circle by one arc is called one degree and is denoted by 1°.

60 seconds (60'') make one minute (1')
60 minutes (60') make one degree (1°)

Circular System:
In Circular System, an angle is measured in radians.

Radian:
A radian is an angle subtended at the center of a circle by an arc whose length is equal to the radius.

Remember:
1 radian ≈ 57.295797°

Arc:
An arc is a portion of the circumference of a circle.

Segment of a circle:
A part of a circle bounded by a chord and an arc is called segment of a circle.

Sector of a circle:
A part of a circle bounded by two radii and an arc is called sector of a circle.

Coterminal Angles:
Two or more than two angles with the same initial and terminal sides are called coterminal angles.

Quadrantal angle:
If the terminal side of an angle in standard position falls on x-axis or y-axis then it is called a Quadrantal angle.


cscθ is the reciprocal of the sinθ.
secθ is the reciprocal of the cosθ.
cotθ is the reciprocal of the tanθ.

Angle of Elevation:
The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

Angle of Depression.
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.




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