We already know that :
In a right angled OAB, where ∠BOA = θ

Sin θ =
[
Perpendicular / Hypotenuse
]
= [^{AB}/_{OB}]

Cos θ =
[
Base / Hypotenuse
]
= [^{OA}/_{OB}]

Tan θ =
[
Perpendicular / Base
]
= [^{AB}/_{OA}]

Cosec θ =
[^{1}/_{sin θ}]
= [^{OB}/_{AB}]

Sec θ =
[^{1}/_{cos θ}]
= [^{OB}/_{OA}]

Cot θ =
[^{1}/_{tan θ}]
= [^{OA}/_{AB}]

Trigonometrical Identities :

Sin^{2} θ + Cos^{2} θ = 1.

1 + Tan^{2} θ = Sec^{2} θ.

1 + Cot^{2} θ = Cosec^{2} θ.

Values of T-ratios :

θ

0°

(π/6) 30°

(π/4) 45°

(π/3) 60°

(π/2) 90°

Sin θ

0

^{1}/_{2}

^{1}/_{√2}

^{√3}/_{2 }

1

Cos θ

1

^{√3}/_{2 }

^{1}/_{√2}

^{1}/_{2}

0

Tan θ

0

^{1}/_{√3}

1

√3

not defined

Angle of Elevation : Suppose a man from a point O
looks up at an object P placed above the level of his eye.
Then the angle which the line of sight makes with the
horizontal through O is called the angle of elevation of
P as seen from O.

∴ Angle of elevation of P from O = ∠AOP

Angle of Depression : Suppose a man from a point
O looks down at an object P, placed below the level of
his eye, then the angle which the line of sight makes
with the horizontal through O, is called the angle of
depression of P as seen from O.