Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(θ - 270°)

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Recall the cosine difference identity: \(\cos(A - B) = \cos A \cos B + \sin A \sin B\).

Apply the identity to the expression \(\cos(\theta - 270^\circ)\) by letting \(A = \theta\) and \(B = 270^\circ\).

Write the expression as \(\cos \theta \cos 270^\circ + \sin \theta \sin 270^\circ\).

Substitute the known values: \(\cos 270^\circ = 0\) and \(\sin 270^\circ = -1\).

Simplify the expression to get a trigonometric function involving only \(\theta\).

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주요 개념

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Cosine of a Difference Identity

The cosine of a difference identity states that cos(A - B) = cos A cos B + sin A sin B. This formula allows you to express the cosine of the difference between two angles in terms of the cosines and sines of the individual angles, which is essential for rewriting expressions like cos(θ - 270°).

Values of Trigonometric Functions at Special Angles

Certain angles, such as 0°, 90°, 180°, 270°, and 360°, have known sine and cosine values. For example, cos 270° = 0 and sin 270° = -1. Knowing these values helps simplify expressions involving these angles, enabling you to rewrite cos(θ - 270°) in terms of cos θ and sin θ.

Simplification of Trigonometric Expressions

After applying identities and substituting known values, simplifying the resulting expression is crucial. This involves combining like terms and reducing the expression to a single trigonometric function of θ, making it easier to interpret or use in further calculations.

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.cos(θ - 270°)