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

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

Identify \(A = 270^\circ\) and \(B = \theta\) in the expression \(\cos(270^\circ + \theta)\).

Apply the identity: \(\cos(270^\circ + \theta) = \cos 270^\circ \cos \theta - \sin 270^\circ \sin \theta\).

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

Substitute these values back into the expression to write it solely in terms of \(\theta\).

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주요 개념

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Cosine of a Sum Identity

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

Special Angle Values

Special angles such as 0°, 90°, 180°, 270°, and 360° have known sine and cosine values. For example, cos 270° = 0 and sin 270° = -1. Using these values simplifies expressions involving these angles, enabling the reduction of cos(270° + θ) to a function involving only θ.

Trigonometric Function Simplification

After applying identities and substituting known values, simplifying the resulting expression involves combining like terms and recognizing standard trigonometric functions. This step ensures the final expression is written solely in terms of θ, as required.

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