# Basic Trigonometry

**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.

## Trigonometric Identities

- 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.

## Solving Trigonometric Equations

- 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.

## Graphs of Trigonometric Functions

- 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.