Basic Trigonometry – A Level Mathematics B (MEI) OCR Revision

Basic Trigonometry in Pure Mathematics

Definitions and Basic Concepts

Understand, remember, and apply the relationship between the sides and angles of a right-angled triangle as defined by the sine (sin), cosine (cos), and tangent (tan) ratios.
Familiarise yourself with the unit circle and use it to relate angles and points on a coordinate plane, to define the sin, cos, and tan of an angle.
Recall and use the reciprocal trigonometric ratios - cosecant (csc), secant (sec), and cotangent (cot), defined respectively as the reciprocals of sin, cos, and tan.

Apply the Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ.
Use double-angle and half-angle identities to simplify and solve trigonometric expressions.
Be familiar with the sum and difference formulas for sin, cos, and tan.

Demonstrate fluency in solving trigonometric equations for a desired range, including those involving multiple angles or compound angles.
Know how to solve trigonometric equations resulting in quadratic forms, such as sin²θ = cos²θ.

Be able to draw and interpret graphs of y = sin x, y = cos x, and y = tan x.
Understand the impact of transformations such as translations, reflections, and stretches on these graphs.
Be able to identify and use period, amplitude, and phase shift of trigonometric functions from their graphs.