MathsFreePrintable

Radians and Wave Oscillation

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Radians and Wave Oscillation worksheet preview
Name:Date:

Radians and Wave Oscillation

Use exact answers in terms of π where possible. Give units for lengths, times and angular frequencies. Assume angles are measured in radians unless a degree symbol is shown.

Angles in radians

A radian is the angle at the centre of a circle subtended by an arc whose length equals the radius. A complete turn is 2π radians, or 360°. For an angle θ in radians, arc length s = rθ.

1.The angle shown is one quarter of a complete turn. Write its size in radians and degrees.
2.A rotating beacon turns through 150°. Convert this angle to radians, simplifying your answer.
3.A pendulum has a length of 1.2 m and swings through an angle of 2π/3 radians. How far does its bob travel along the arc? Use s = rθ.

Describing oscillations

A sinusoidal oscillation can be written y = A sin(ωt), where A is the amplitude, ω is the angular frequency in radians per second, and t is time in seconds. Its period is T = 2π/ω. Frequency f is measured in hertz, with ω = 2πf.

4.A speaker cone completes 5 oscillations each second. Calculate its angular frequency in radians per second.
5.For the oscillation y = 3 sin(2πt), state the amplitude, angular frequency and period. Include suitable units for the period and angular frequency.
6.A wave is modelled by y = 2 cos(πt). What is its value at t = 0.5 s?
  • 0
  • 1
  • −1
  • 2
7.Sketch y = sin(t) for 0 ≤ t ≤ 2π. Mark the horizontal-axis values 0, π/2, π, 3π/2 and 2π, and show the maximum and minimum values.
8.A wave has angular frequency 4π rad/s. How long does one complete oscillation take?
9.A Ferris wheel turns at a constant angular speed of 0.5 rad/s. Calculate the time taken for one complete revolution. Give your answer to 1 decimal place.
10.Explain why radians are convenient in equations for waves and oscillations. Include one relevant mathematical relationship.

3 printable pages

  • Radians and Wave Oscillation, page 1 of 3: Angles in radians

    Page 1

  • Radians and Wave Oscillation, page 2 of 3: Describing oscillations

    Page 2

  • Radians and Wave Oscillation, page 3 of 3: 9. A Ferris wheel turns at a constant angular speed of 0.5 rad/s. Calculate the time…

    Page 3

About This Worksheet

Free in Kuraplan

Sign up free, grab the PDF, and customize it for your class.

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free
No credit card Curriculum-aligned Under 60 seconds