Class notes Trigonometry math cbse MATHEMATICS (STANDARD)

Introduction To Trigonometry
Trigonometric Ratios
Opposite & Adjacent Sides in a Right Angled Triangle

In the ΔABC right-angled at B, BC is the side opposite to ∠A, AC is the hypotenuse and AB
is the side adjacent to ∠A.




Trigonometric Ratios

For the right ΔABC , right angled at ∠B, the trigonometric ratios of the ∠A are as follows:
opposite side BC
sinA = =
hypotenuse AC

adjacent side
AB
cosA = =
hypotenuse AC

opposite side
BC
tanA = =
adjacent side AB

hypotenuse AC
cosecA = =
opposite side BC

hypotenuse AC
secA = =
adjacent side AB

adjacent side
AB
cotA = =
opposite side BC

, Visualisation of Trigonometric Ratios Using a Unit Circle

Draw a circle of unit radius with the origin as the centre. Consider a line segment OP joining
a point P on the circle to the centre which makes an angle θ with the x-axis. Draw a
perpendicular from P to the x-axis to cut it at Q.

PQ PQ
sinθ = = = PQ
OP 1

OQ OQ
cosθ = = = OQ
OP 1

PQ sinθ
tanθ = =
OQ cosθ

OP 1
cosecθ = =
PQ PQ

OP 1
secθ = =
OQ OQ

OQ cosθ
cotθ = =
PQ sinθ