Trigonometry studies the relationship between angles and sides of a triangle. In Class 10 Maths, it focuses on right-angled triangles, trigonometric ratios, identities, and angle values. These concepts help students calculate heights, distances, and unknown sides using sine, cosine, and tangent functions. Trigonometry also introduces exact values, standard angles, and identities that simplify complex expressions into solvable forms. CBSE uses trigonometry to test logical thinking, formula application, and accuracy across numerical problems.

In this blog, you will learn the important trigonometry formulas for CBSE Class 10 Maths, including trigonometric ratios, identities, and standard angle values, and understand what each formula helps you calculate.

Important Trigonometry Formulas for Class 10 Maths

Trigonometry formulas help students calculate angles, side lengths, and relationships inside a right-angled triangle. These formulas convert geometric problems into numerical steps using trigonometric ratios and identities. In CBSE Class 10 Maths, trigonometry plays a key role in solving height and distance problems, simplifying expressions, and proving identities. Mastery of these formulas improves speed, accuracy, and scoring consistency in board exams.

Trigonometric Ratio Abbreviations

The table below shows the standard abbreviations and meanings of trigonometric ratios used in Class 10 Maths.

Trigonometric Ratio Formulas

Basic Trigonometric Ratios

• sin A = Perpendicular / Hypotenuse
• cos A = Base / Hypotenuse
• tan A = Perpendicular / Base
  

Trigonometric Identities

Pythagorean Identities

• sin² A + cos² A = 1
• 1 + tan² A = sec² A
• 1 + cot² A = cosec² A
  

Derived Identities

• sin² θ = 1 − cos² θ
• cos² θ = 1 − sin² θ
• sec² θ − tan² θ = 1
• cosec² θ − cot² θ = 1
  

Reciprocal Identities

• sin θ cosec θ = 1
• cos θ sec θ = 1
• tan θ cot θ = 1
  

Complementary Angle Identities

• sin (90° − A) = cos A
• cos (90° − A) = sin A
• tan (90° − A) = cot A
• cot (90° − A) = tan A
• sec (90° − A) = cosec A
• cosec (90° − A) = sec A

Trigonometric Table (Standard Angle Values)

This trigonometric table helps students find the values of trigonometric ratios for standard angles 0°, 30°, 45°, 60°, and 90°.

Real Life Applications of Trigonometry Formulas

• Trigonometry helps measure heights and distances when direct measurement is not possible. Engineers use angle of elevation and trigonometric ratios to calculate the height of buildings, towers, and mountains.
• Astronomers use trigonometry to estimate distances between Earth and celestial objects. Stellar parallax applies angular measurement to calculate the distance of stars and planets without physical travel.
• Sine and cosine functions describe periodic motion. Physics uses these functions to model sound waves, light waves, and alternating electrical currents.
• Construction and civil engineering use trigonometry to design slopes, roofs, staircases, bridges, and road gradients. Accurate angle calculation ensures structural stability.
• Navigation systems rely on trigonometry to determine direction, position, and distance. Ships, aircraft, and satellites calculate routes using angular measurements.
• Computer graphics and video games apply trigonometric formulas to control motion, rotation, and camera angles in two dimensional and three dimensional spaces.
• Trigonometry supports satellite communication and GPS technology. Position tracking depends on angular data and distance calculations.
• Scientific research uses trigonometry wherever distance, motion, or direction requires numerical proof. Most measurement based discoveries depend on trigonometric calculation.

Tips to Memorize Trigonometry Formulas for Class 10

• Understand what each ratio represents in a right-angled triangle. Link sine, cosine, and tangent to sides, not symbols.
• Learn formulas by grouping them. Memorize basic ratios first, then identities, then complementary angle relations.
• Rewrite formulas daily instead of reading them. Writing improves recall speed in exams.
• Use the standard angle table to verify identities. Checking values at 30°, 45°, and 60° builds confidence.
• Practice identity-based questions regularly. These questions test formula memory and logical application together.
• Revise formulas before problem-solving. Clear recall reduces calculation errors during exams.

Trigonometry Formula Example 

Question

If sin (A + 20°) = cos (2A), where A is an acute angle, find the value of A.

Solution

Use the complementary angle identity:
cos θ = sin (90° − θ)

Rewrite the given equation:
sin (A + 20°) = sin (90° − 2A)

Equate the angles:
A + 20° = 90° − 2A

Solve the equation:
3A = 70°
A = 70° ÷ 3
A ≈ 23.33°