CBSE Grade 10 Maths Chapter 8 - Introduction to Trigonometry

What is Meant by Trigonometry?

The word ‘trigonometry’ is derived from the Greek words ‘tri’(meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure).

In fact, trigonometry is the study of relationships between the sides and angles of a triangle.

Right-Angled Triangle

A right-angled triangle has one angle of measure 90° and 2 acute angles.

The right angle is indicated by the little box in the corner.
The other angle that we (usually) know is indicated by θ (theta).
The side opposite the right angle, which is the longest side, is called the hypotenuse.
The side opposite θ is called the opposite side.
The side next to θ which is not the hypotenuse is called the adjacent side.
Also,

Position of Sides with respect to ∠A of ⃤ ABC

Side AC

- Longest side of the Triangle

- Hypotenuse of the Right Angled Triangle

Side AB

- It is part of ∠A
- Side Adjacent to ∠A

Side BC

- It faces or is opposite to ∠A
- Side Opposite to ∠A

Trigonometric Ratios

In a right angle triangle, the ratio of its side and the acute angles is the trigonometric ratios of the angles.
Trigonometric ratios with respect to ∠A

Note :

If we take ∠C as acute angle then

BC will be base
AB will be perpendicular.
Hypotenuse remains the same i.e. AC

So the ratios will be according to that only.

If the angle is same then the value of the trigonometric ratios of the angles remain the same whether the length of the side increases or decreases.

In a right angled triangle, the hypotenuse is the longest side so

sin A or cos A will always be less than or equal to 1
the value of sec A or cosecant A will always be greater than or equal to 1.

Reciprocal Relationship between Trigonometric Ratios

Cosec A, sec A, and cot A are the reciprocals of sin A, cos A, and tan A respectively.

Trigonometric Ratios of Some Specific Angles

Trigonometric Ratios of Complementary Angles

If the sum of two angles is 90° then, it is called Complementary Angles.
In a right-angled triangle, one angle is 90 °, so the sum of the other two angles is also 90° or they are complementary angles.so the trigonometric ratios of the complementary angles will be -

sin (90° – A) = cos A

cos (90° – A) = sin A

tan (90° – A) = cot A

cot (90° – A) = tan A

sec (90° – A) = cosec A

cosec (90° – A) = sec A