2026 Oxfordshire Math Y11 Graphs of Trigonometric Functions

Which of these values cannot be the sine of an angle?

• 0

• -0.9

• ⅔

• 1.2

Answer explanation

The sine of an angle must be between -1 and 1. While 0, -0.9, and ⅔ are valid sine values, 1.2 exceeds this range and cannot be the sine of any angle.

Which of these values cannot be the cosine of an angle?

• -1

• 3

• 0.7

• -0.04

Answer explanation

The cosine of an angle must be between -1 and 1. Therefore, the value 3 cannot be the cosine of any angle, as it exceeds this range.

Here is part of the curve y = sin(x) (a) Write down the coordinates of the point A.

• (90, 1)

• (0, 0)

• (180, -1)

• (45, 0.707)

Answer explanation

The point A on the curve y = sin(x) corresponds to x = 90 degrees, where sin(90) = 1. Thus, the coordinates of point A are (90, 1), making (90, 1) the correct choice.

Here is part of the curve y = sin(x) (b) Write down the coordinates of the point B.

• (270, -1)

• (180, 1)

• (90, 0)

• (360, 0)

Answer explanation

The point B on the curve y = sin(x) corresponds to x = 270 degrees, where sin(270) = -1. Thus, the coordinates of point B are (270, -1), making this the correct choice.

Here is part of the curve y = cos(x) (a) Write down the coordinates of the point A.

• (0, 1)

• (1, 0)

• (0, 0)

• (1, 1)

Answer explanation

The point A on the curve y = cos(x) corresponds to x = 0. At this point, y = cos(0) = 1, giving the coordinates (0, 1). Thus, the correct answer is (0, 1).

Here is part of the curve y = cos(x) (b) Write down the coordinates of the point B.

• (180, -1)

• (90, 1)

• (0, 0)

• (180, 1)

Answer explanation

The point B corresponds to x = 180 degrees on the curve y = cos(x). At this point, cos(180) = -1, so the coordinates are (180, -1), making this the correct choice.

Which of the following graphs represents y = cos(x) for 0° ≤ x ≤ 360°?

• A graph starting at y = 1 when x = 0°, reaching y = -1 at x = 180°, and returning to y = 1 at x = 360°.

• A graph starting at y = 0 when x = 0°, reaching y = 1 at x = 90°, and returning to y = 0 at x = 360°.

• A graph starting at y = -1 when x = 0°, reaching y = 1 at x = 180°, and returning to y = -1 at x = 360°.

• A graph starting at y = 1 when x = 0°, remaining constant at y = 1 for all x.

Answer explanation

The correct graph for y = cos(x) starts at y = 1 when x = 0°, decreases to y = -1 at x = 180°, and returns to y = 1 at x = 360°. This matches the first answer choice.

The graph of y = sin(x) for 0° ≤ x ≤ 360° is:

• A wave that starts at 0, reaches 1 at 90°, returns to 0 at 180°, reaches -1 at 270°, and returns to 0 at 360°.

• A straight line increasing from 0 to 360.

• A parabola opening upwards.

• A constant line at y = 1.

Answer explanation

The graph of y = sin(x) is a wave that starts at 0, peaks at 1 (90°), returns to 0 (180°), dips to -1 (270°), and returns to 0 at 360°. This matches the correct choice.

Which of the following graphs represents y = tan(x) for 0° ≤ x ≤ 360°?

• A graph with vertical asymptotes at x = 90° and x = 270°, and repeating wave-like pattern between them.

• A graph with a straight line passing through the origin.

• A graph with a sine wave oscillating between -1 and 1.

• A graph with a parabola opening upwards.

Answer explanation

The correct graph for y = tan(x) shows vertical asymptotes at x = 90° and x = 270°, indicating where the function is undefined. The repeating wave-like pattern between these asymptotes represents the periodic nature of the tangent function.

Which graph is y = sin(x)?

• Graph 1

• Graph 2

• Graph 3

Answer explanation

Graph 1 represents the function y = sin(x), showing its characteristic wave pattern with peaks at π/2 and troughs at 3π/2. The other graphs do not match this sine wave behavior.