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# 3.15: Triple-Angle Formulas and Linear Combinations

Difficulty Level: At Grade Created by: CK-12
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Practice Triple-Angle Formulas and Linear Combinations

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Estimated10 minsto complete
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### Vocabulary Language: English

TermDefinition
Linear Combination A linear combination is a set of terms that are added or subtracted from each other with a multiplicative constant in front of each term.
Triple Angle Identity A triple angle identity (also referred to as a triple angle formula) relates a trigonometric function of three times an argument to a set of trigonometric functions, each containing the original argument. Examples include: the Triple Angle Formula for Sine $\text{sin} (3\theta) = 3 \text{sin} \theta - 4 \text{sin}^3 \theta$, the Triple Angle Formula for Cosine $\text{cos} (3 \theta) = -3 \text{ cos} \theta + 4 \text{ cos}^3 \theta$, and the Triple Angle Formula for Tangent $\text{tan} (3 \theta) = \frac{3 \text{ tan} \theta - \text{ tan}^3 \theta}{1 - 3 \text{ tan}^2 \theta}$.

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