Class notes mathematics

Here are short & clear notes on Trigonometric Functions (perfect for JEE / Class 11 quick
revision):



📘 1. Basic Trigonometric Ratios

For a right triangle with angle θ:
[
\sin θ = \frac{P}{H}, \quad \cos θ = \frac{B}{H}, \quad \tan θ = \frac{P}{B}
]
[
\csc θ = \frac{1}{\sin θ}, \quad \sec θ = \frac{1}{\cos θ}, \quad \cot θ = \frac{1}{\tan θ}
]



📗 2. Trigonometric Identities

1. Pythagorean identities:
o (\sin^2θ + \cos^2θ = 1)
o (1 + \tan^2θ = \sec^2θ)
o (1 + \cot^2θ = \csc^2θ)
2. Reciprocal relations:
o (\sin θ = 1/\csc θ), (\cos θ = 1/\sec θ), (\tan θ = 1/\cot θ)
3. Quotient relations:
o (\tan θ = \sin θ / \cos θ)
o (\cot θ = \cos θ / \sin θ)




📙 3. Signs of Trigonometric Functions (Quadrants)

Quadrant sin cos tan
I + + +
II + – –
III – – +
IV – + –

🔹 Rule: “All Students Take Calculus”
(I: All +, II: sin +, III: tan +, IV: cos +)



📒 4. Trigonometric Functions of Allied Angles

 (\sin(90° - θ) = \cos θ)
 (\cos(90° - θ) = \sin θ)
 (\tan(90° - θ) = \cot θ)