Trigonometry

Trigonometry

Trigonometric Ratios and Angles

• Understand the definitions of sin, cos and tan for all angles in terms of a unit circle.
• Be able to use cot, sec and cosec, and know how they relate to sin, cos and tan.
• Familiarise yourself with the exact values of sin, cos and tan for commonly used angles.
• Understand the periodicity, amplitude and frequency of trigonometric functions.

Solving Trigonometric Equations

• Solve simple equations involving trigonometric functions.
• Familiarise with and apply the sine rule, cosine rule and the formula for area of a triangle for solving more complex problems.
• Understand the process of finding general solutions to trigonometric equations.
• Know how to solve trigonometric equations using auxiliary angles.

Inverse Trigonometric Functions

• Understand the definitions and properties of the inverse trigonometric functions, sin⁻¹, cos⁻¹ and tan⁻¹.
• Know how to apply inverse trigonometric functions to calculate angles in practical situations.

Trigonometric Identities

• Recall and apply the Pythagorean identities in terms of sin, cos and tan.
• Understand and utilise the double angle identities and addition and subtraction identities.
• Familiarise with and apply the product-to-sum and sum-to-product identities.

Trigonometric Series

• Practice and understand how to express sin and cos as complex exponentials using Euler’s formula.
• Know how to derive and apply the trigonometric series representations for sin, cos and tan.

Trigonometry in Real Life Contexts

• Understand and be able to solve practical problems involving height and distance using trigonometric ratios.
• Apprehend how trigonometry can be utilised to solve problems in physics, such as those involving waves and oscillations.
• Be able to apply the trigonometric understanding in engineering scenarios such as in building bridges and towers.