About Angle Difference Formula
By representing the trigonometric ratios of some specific non-standard angles as the difference between two standard angles,
By representing the trigonometric ratios of some specific non-standard angles as the difference between two standard angles, angle difference formulae are utilised to find them. Angle difference identities are another name for these. Angle sum formulas exist in addition to angle difference formulas.
What is Angle Difference Formula?
The values of trigonometric functions of standard angles are already known from the trigonometric table. Using the trigonometric table, we may determine the exact values of sin 90°, cos 45°, cosec 30°, and so on. What are the values for sin 75°, cos 15°, tan 105°, and other angles?
| Trigonometry Ratios Table | ||||||||
| Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| Angles (In Radians) | 0° | π/6° | π/4° | π/3° | π/2° | π° | 3π/2° | 2π° |
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
| tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
| cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
| cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
| sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
The angle difference and angle sum formulas can be used to find these.
The angle difference formulas are listed below.
sin (A+B) = sin A cos B + cos A sin B
sin (A-B) = sin A cos B - cos A sin B
cos (A+B) = cos A cos B - sin 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)
tan (A-B) = (tan A - tan B)/(1 + tan A tan B)
Get the List of Maths formulas.
Find pdf of Angle Difference Formula
Frequently Asked Questions
The Angle Difference Formula in trigonometry helps calculate the sine, cosine, and tangent of the difference between two angles. The formulas are:
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sin(A - B) = sin A cos B - cos A sin B
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cos(A - B) = cos A cos B + sin A sin B
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tan(A - B) = (tan A - tan B) / (1 + tan A tan B)
These formulas are useful in simplifying trigonometric expressions and solving problems related to angles.
The Angle Difference Formula is commonly used to:
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Simplify complex trigonometric expressions.
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Derive exact values of trigonometric functions for specific angles.
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Solve problems in physics, engineering, and geometry involving angles.
For example, using cos(60° - 30°):
cos 30° = cos 60° cos 30° + sin 60° sin 30° = (1/2 × √3/2) + (√3/2 × 1/2) = 1/2.
The Angle Difference Formula is applied in:
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Navigation & GPS systems to calculate direction changes.
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Physics & Engineering for wave calculations and signal processing.
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Astronomy for determining angular distances between celestial objects.
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Surveying & Architecture for angle measurements and land mapping.