Trigonometric graphs
AQA GCSE Maths revision on Trigonometric graphs. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
-
Question 1
Why does the graph of y = sin(x) repeat its pattern every 360 degrees?
- A) Because the sine function is based on the y-coordinate of a point moving around a full circle.
- B) Because the sine function is based on the x-coordinate of a point moving around a full circle.
- C) Because the maximum value of the sine function is 360.
- D) Because the sine function is only defined for angles between 0 and 360 degrees.
Show answer
Answer: Because the sine function is based on the y-coordinate of a point moving around a full circle.
Trigonometric functions are derived from the unit circle where the angle x represents the rotation from the positive x-axis. Since a full rotation is 360 degrees, the y-coordinate returns to its starting position after this interval, causing the wave pattern to repeat. This property is known as periodicity.
-
Question 2
A student claims that the graph of y = cos(x) is identical to y = sin(x) just shifted horizontally. What is the name of this relationship?
Show answer
Answer: Phase shift
The sine and cosine graphs are both periodic waves with the same amplitude and frequency. By shifting the sine graph 90 degrees to the left, it perfectly overlaps with the cosine graph. This horizontal displacement is referred to as a phase shift.
-
Question 3
If the graph of y = sin(x) is transformed into y = 3sin(x), what geometric feature of the graph has changed?
- A) The period of the wave.
- B) The phase shift of the wave.
- C) The amplitude of the wave.
- D) The horizontal starting point of the wave.
Show answer
Answer: The amplitude of the wave.
The coefficient 'a' in the form y = a*sin(x) determines the vertical stretch of the graph from the x-axis. Increasing this value from 1 to 3 increases the maximum height and decreases the minimum depth, which is defined as the amplitude.
Want to test yourself on the remaining cards for this topic?
13 more questions on Trigonometric graphs — plus mistakes tracking and spaced repetition across the whole Maths spec.