Trigonometric Functions — Test

Question 16 • Algebra II

Which of the following is the graph of y is equal to cosine of 2 x ?

Answer

Image with description A coordinate plane. The graph starts and rises to (negative 24 pi comma 1). It starts to fall through (negative 21 pi comma 0) to (negative 18 pi comma negative 1). It then rises through (negative 15 pi comma 0) to (negative 12 pi comma 1). It then falls through (negative 9 pi comma 0) to (negative 6 pi comma negative 1). It then rises through (negative 3 pi comma 0) to (0 comma 1). It then falls through (3 pi comma 0) to (6 pi comma negative 1). It then rises though (9 pi comma 0) to (12 pi comma 1). It then falls through (15 pi comma 0) to (18 pi comma negative 1). It then rises through (21 pi comma 0) to (24 pi comma 1).

Image with description A coordinate plane. The graph starts and rises to (negative 8 pi comma 1). It starts to fall through (negative 7 pi comma 0) to (negative 6 pi comma negative 1). It then rises through (negative 5 pi comma 0) to (negative 4 pi comma 1). It then falls through (negative 3 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (negative pi comma 0) to (0 comma 1). It then falls through (pi comma 0) to (2 pi comma negative 1). It then rises though (3 pi comma 0) to (4 pi comma 1). It then falls through (5 pi comma 0) to (6 pi comma negative 1). It then rises through (7 pi comma 0) to (8 pi comma 1).

Image with description A coordinate plane. The graph starts and rises to (negative 2 pi comma 1). It starts to fall through (negative 7 pi over 4 comma 0) to (negative 3 pi over 2 comma negative 1). It then rises through (negative 5 pi over 4 comma 0) to (negative pi comma 1). It then falls through (negative 3 pi over 4 comma 0) to (negative pi over 2 comma negative 1). It then rises through (negative pi over 4 comma 0) to (0 comma 1). It then falls through (pi over 4 comma 0) to (pi over 2 comma negative 1). It then rises though (3 pi over 4 comma 0) to (pi comma 1). It then falls through (5 pi over 4 comma 0) to (3 pi over 2 comma negative 1). It then rises through (7 pi over 4 comma 0) to (2 pi comma 1).

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It then falls through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

Explanation

The graph of y = cos(2x) has amplitude 1 and period 2π/2 = π. It starts at y = 1 when x = 0, reaches y = −1 at x = π/2, and returns to y = 1 at x = π. Choice C has these values and repeats every π, so it is the graph of y = cos(2x).

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