Trigonometric Functions for JEE and CBSE board exams

Trigonometric ratios

• Sine (sin θ) = Length of opposite side / Hypotenuse
• Cosine (cos θ) = Length of adjacent side / Hypotenuse
• Tangent (tan θ) = Opposite side / Adjacent side

Trigonometric identities

• Pythagorean identity: sin^2 θ + cos^2 θ = 1
• Sum and difference formulas:
• sin(A ± B) = sin A cos B ± cos A sin B
• cos(A ± B) = cos A cos B ∓ sin A sin B
• tan(A ± B) = (tan A ± tan B) / (1∓ tan A tan B)
• Product-to-sum formulas:
• sin A cos B = ½ (sin(A + B) + sin(A - B))
• cos A sin B = ½ (sin(A + B) - sin(A - B))

Graphs of trigonometric functions

• Sine: A periodic wave that oscillates between -1 and 1.
• Cosine: A periodic wave that oscillates between -1 and 1, shifted by π/2 radians from the sine curve.
• Tangent: A non-periodic wave that increases or decreases without bound as θ approaches π/2 or -π/2.

Inverse trigonometric functions

• Arcsine (sin^-1 θ): The angle whose sine is θ.
• Arccosine (cos^-1 θ): The angle whose cosine is θ.
• Arctangent (tan^-1 θ): The angle whose tangent is θ.

Applications of trigonometry

• Finding the height of a building using trigonometric ratios.
• Determining the distance to a star by measuring the angle of parallax.
• Calculating the angle of elevation/depression of an object.