Fill in the blank(s) to correctly complete each sentence.
The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x unit(s) to the __ (right/left).

검증된 단계별 안내

Recall that the function y = cos(x - c) represents a horizontal shift of the basic cosine graph y = cos x by c units.

If the function is y = cos(x - \(\frac{\pi}{6}\)), the graph is shifted horizontally by \(\frac{\pi}{6}\) units.

Since the expression inside the cosine is (x - \(\frac{\pi}{6}\)), this corresponds to a shift to the right by \(\frac{\pi}{6}\) units.

Therefore, the graph of y = cos(x - \(\frac{\pi}{6}\)) is obtained by shifting the graph of y = cos x \(\frac{\pi}{6}\) unit(s) to the right.

Fill in the blanks with: "\(\frac{\pi}{6}\)" and "right".

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Horizontal Phase Shift in Trigonometric Functions

A horizontal phase shift occurs when the input variable x in a trigonometric function is replaced by (x - c), shifting the graph horizontally. If the function is y = cos(x - c), the graph shifts c units to the right; if y = cos(x + c), it shifts c units to the left.

Understanding the Argument of the Cosine Function

The argument inside the cosine function, such as (x - π/6), determines the horizontal position of the wave. Modifying this argument translates the graph along the x-axis without changing its shape or amplitude.

Graphical Interpretation of Trigonometric Transformations

Graph transformations help visualize how changes in the function's formula affect its graph. Recognizing shifts, stretches, and reflections allows one to predict and sketch the new graph accurately.

Fill in the blank(s) to correctly complete each sentence.The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).