Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Trigonometric ratios are a fundamental topic in JEE Maths, forming the base for coordinate geometry, calculus, and physics applications. The study of sine, cosine, tangent, cotangent, secant, and cosecant is essential for solving JEE Main and Advanced problems efficiently. At StudentBro.in, we provide a comprehensive guide covering definitions, formulas, properties, examples, and practice problems to help JEE aspirants excel in trigonometric ratios.
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Trigonometric ratios relate the angles of a right triangle to the ratios of its sides. For an angle θ in a right triangle:
Sine (sin θ) = Opposite / Hypotenuse
Cosine (cos θ) = Adjacent / Hypotenuse
Tangent (tan θ) = Opposite / Adjacent
Cotangent (cot θ) = Adjacent / Opposite
Secant (sec θ) = Hypotenuse / Adjacent
Cosecant (csc θ) = Hypotenuse / Opposite
Example: For a right triangle with sides 3, 4, 5 and θ opposite 3 → sin θ = 3/5, cos θ = 4/5, tan θ = 3/4
csc θ = 1 / sin θ
sec θ = 1 / cos θ
cot θ = 1 / tan θ
These identities help simplify complex trigonometric expressions in JEE problems.
sin² θ + cos² θ = 1
1 + tan² θ = sec² θ
1 + cot² θ = csc² θ
Useful in deriving formulas, solving equations, and simplifying expressions
Example: sin² 30° + cos² 30° = (1/2)² + (√3/2)² = 1
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)
Essential for solving trigonometric equations in JEE Main & Advanced
sin 2A = 2 sin A cos A
cos 2A = cos² A - sin² A = 2 cos² A - 1 = 1 - 2 sin² A
tan 2A = 2 tan A / (1 - tan² A)
sin² (A/2) = (1 - cos A)/2, cos² (A/2) = (1 + cos A)/2
Useful for integrals, equations, and simplification
0°, 30°, 45°, 60°, 90° are frequently asked in exams
Memorize sin, cos, tan values:
sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
sin 45° = √2/2, cos 45° = √2/2, tan 45° = 1
sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3
Allows quick calculation without a calculator
All Students Take Calculus (ASTC) mnemonic:
Quadrant I: All positive
Quadrant II: sin positive
Quadrant III: tan positive
Quadrant IV: cos positive
Helps in sign determination for angles
sin⁻¹ x, cos⁻¹ x, tan⁻¹ x give angles for given trigonometric values
Range is restricted to maintain function properties
sin⁻¹ x: [-π/2, π/2]
cos⁻¹ x: [0, π]
tan⁻¹ x: (-π/2, π/2)
Used in solving equations and coordinate geometry
Used to calculate heights, distances, and angles
Applied in physics, mechanics, and JEE coordinate problems
Important for sine rule, cosine rule, and area of triangle
Simplify expressions using reciprocal, Pythagorean, sum-difference, double-angle identities
Solve equations like sin θ + cos θ = 1, tan² θ - 3 tan θ + 2 = 0
Regular practice ensures speed and accuracy in JEE exams
Memorize all standard trigonometric formulas and ratios
Draw right triangles to visualize ratios
Use ASTC for quadrant signs
Solve previous year JEE trigonometry questions for speed
Apply identities systematically to simplify complex problems
At StudentBro.in, students can access:
Step-by-step explanations for sine, cosine, tangent, cotangent, secant, cosecant
Worked examples for angles, standard triangles, and identities
Practice questions with solutions and shortcuts
Tips for quick problem-solving and exam strategy
Revision notes for last-minute preparation
Find sin θ, cos θ, tan θ for θ = 45°
Solve sin² θ + 3 sin θ cos θ - cos² θ = 0
Find tan(A + B) if tan A = 1/2, tan B = 1/3
Prove 1 + cot² θ = csc² θ
Find sin 2A, cos 2A if sin A = 3/5
Regular practice improves accuracy, speed, and confidence in solving trigonometric ratio problems in JEE exams.
Trigonometric Ratios are a vital chapter in JEE Maths. Understanding sine, cosine, tangent, cotangent, secant, cosecant, identities, and formulas allows students to solve coordinate geometry, calculus, and physics-related problems efficiently. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making trigonometry simple, practical, and exam-oriented.
Mastering this topic ensures students can tackle trigonometric equations, identities, and angle problems confidently in both JEE Main and Advanced exams.
