Addition & Subtraction formula for Sine, Cosine, & Tangent Math Activities

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Definition

The addition and subtraction formulas for sine, cosine, and tangent are trigonometric identities that allow us to find the exact value of a trigonometric function involving the sum or difference of two angles, such as $\sin(A \pm B)$sin(A±B), $\cos(A \pm B)$cos(A±B), and $\tan(A \pm B)$tan(A±B). These formulas express the trigonometric function of a combined angle in terms of the trigonometric functions of the individual angles.

Summary

The addition and subtraction formulas are essential tools in trigonometry because they help simplify expressions, evaluate trigonometric functions without a calculator, and solve trigonometric equations and identities. They are especially useful when angles like $15^\circ$, $75^\circ$, or $\frac{\pi}{12}$12π​ can be written as the sum or difference of special angles.

A key point to remember is that sine keeps the same sign, cosine changes the sign, and tangent follows the same sign pattern as sine in the numerator while changing in the denominator.

These formulas form the foundation for many trigonometric activities, including proving identities, solving equations, and evaluating exact trigonometric values, making them a crucial topic in advanced algebra and precalculus.

Addition & Subtraction formula for Sine, Cosine, & Tangent Math Activities

This is a fantastic bundle which includes 10 activities with answer guides about the Addition & Subtraction formula for Sine, Cosine, & Tangent. All our worksheets are completely editable so can be tailored for your curriculum and target audience.

Resource Examples

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Worksheets Activities Included

•  Formula Identification
• Exact Value – Sine
• Exact Value – Cosine
• Exact Value – Tangent
• Fill in the Missing Steps
• Match the Expression
• Error Analysis
• Prove an Identity
• Mixed Practice
• Challenge Problem