Trigonometry (AS Unit 1: Pure Mathematics A) — WJEC A-Level Mathematics
Test yourself on Trigonometry (AS Unit 1: Pure Mathematics A) with WJEC A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Trigonometry (AS Unit 1: Pure Mathematics A) explained
The graphs of y = sin x and y = cos x are continuous waves with an amplitude of 1 and a period of 360° (or 2π radians).
Read the full explanation
The sine graph passes through the origin (0, 0), exhibiting rotational symmetry of order 2 about (0, 0) and line symmetry about peaks x = 90° and troughs x = 270°. The cosine graph has a peak at (0, 1), showing line symmetry about the y-axis (x = 0) and rotational symmetry about intercepts (90°, 0) and (270°, 0). The graph of y = tan x has a period of 180° (or π radians), passes through (0, 0) with rotational symmetry, and possesses vertical asymptotes at x = ±90°, ±270°, etc. Periodicity means sin(x + 360°) = sin x, cos(x + 360°) = cos x, and tan(x + 180°) = tan x, which is crucial for generating all solutions to equations in an interval.
Your focus
- Sketch the graphs of sine, cosine, and tangent over specified angular intervals.
- Identify lines of symmetry, rotational symmetry, amplitude, and periodicity of trigonometric curves.
- Use graphical symmetries to deduce all solutions to trigonometric equations in an interval.
Trigonometry (AS Unit 1: Pure Mathematics A) exam tips
Marking Points
- sketching one or more full periods of sine, cosine, or tangent with key coordinates labelled
- identifying the amplitude and period of transformed trigonometric waves
- using rotational or reflectional symmetry to find secondary angles in equation solving
Examiner Tips
- 💡Sketch a standard wave across the requested interval before solving any trigonometric equation.
- 💡Mark coordinates of all peaks, troughs, and axis intercepts clearly on sketches.
Common Mistakes
- drawing tangent graphs with a period of 360° instead of 180°
- misplacing intercepts or peaks when sketching shifted trigonometric graphs