Cambridge O Level Additional Mathematics · Syllabus 4037 · Trigonometry
Amplitude and Period
What is Amplitude and Period?
For a sine or cosine graph of the form y = a sin bx + c or y = a cos bx + c, the amplitude is the modulus of a, which is half the vertical distance between the maximum and the minimum, and the period is the horizontal length of one complete cycle, equal to 360 degrees divided by the modulus of b or two pi divided by the modulus of b. The centre line is y = c, the maximum is c plus the modulus of a and the minimum is c minus the modulus of a. A tangent graph has no amplitude because it is unbounded, and its period is 180 degrees divided by the modulus of b, or pi divided by the modulus of b.
This definition is part of the Trigonometry chapter in Cambridge O Level Additional Mathematics.
Amplitude and Period in context
Trigonometry in Additional Mathematics is the study of six functions — \(\sin\), \(\cos\), \(\tan\), \(\sec\), \(\operatorname{cosec}\) and \(\cot\) — defined for an angle of any size, not just an acute angle in a right-angled triangle. The unit circle supplies the sign of each function in each quadrant, the graphs supply amplitude and period, and three supplied identities let you rewrite any equation in terms of a single function. Every question then reduces to the same discipline: find one reference angle, use quadrant signs and periodicity to generate all the angles, and keep only those inside the stated domain.