Trigonometry of General Triangles and Trigonometric Functions — Test

Question 10 • Mathematics III

Which is the graph of y is equal to cosine of x plus 3 ?

Answer

Image with description A coordinate plane. The graph starts and rises to (0 comma 6). It starts to fall through (pi over 2 comma 3) to (pi comma 0). It then rises through (3 pi over 2 comma 3) to (2 pi comma 6).

Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 6 to 2. The wave reaches a maximum at (0 comma negative 2), drops to a minimum at (pi comma negative 4), and rises again to a maximum at (2 pi comma negative 2).

Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 2 to 6. The wave reaches a maximum at (0 comma 4), drops to a minimum at (pi comma 2), and rises again to a maximum at (2 pi comma 4).

Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 4 to 4. The wave reaches a maximum at (0 comma 3), drops to a minimum at (pi comma negative 3), and rises again to a maximum at (2 pi comma 3).

Explanation

For y = cos(x) + 3, the cosine graph is shifted up 3 units. Since cos(0) = 1 and cos(π) = −1, the graph has a maximum of 4 at x = 0 and a minimum of 2 at x = π; it returns to 4 at x = 2π. Choice D shows these points.

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