# Trigonometry and Trigonometric Graphs (A level)

This is a resource package of resources to aid the teaching and learning of trigonometry and the exploration of the graphs of trigonometric functions post 16

### Trigonometry 2

In this RISP activity, **Radians and Degrees,** students are set the task of finding an angle whose sine value is the same whether measured in radians or degrees. Solving the problem leads to further discussion about the relationship between radians and degrees and general trigonometric equations.

A second RISP activity,** Generating the Compound Angle Formula**, requires students to generate a function given certain components and graph the resultant function. The activity leads to the compound angle formulae for sine and cosine.

### Sometimes, Always, Never

One of three activities produced by Susan Wall designed to provide the opportunity for students to explore the concepts involved and to highlight any misconceptions by discussing whether the statements presented can sometimes be true, are always true or can never be true.

Trigonometry: is the same activity as the algebra activity using different statements. Students are presented with a set of statements appropriate to their stage of learning. Some of the statements will be familiar such as sin^{2}(x) + cos^{2}(x) = 1, whilst others involving sec and cosec may only be met later in the course.

### Thinking Questions

This resource contains a number of open–ended questions which explore understanding and allow a variety of approaches. Each question is easily accessible but can be extended to make a more complex problem. Students are required to justify their answer and, where possible, generalise their answer. Students require problem solving skills and reasoning skills to tackle the problems; trial and error alone will not be sufficient.

Trigonometric functions: one problem exploring translations of sine and cosine graphs.

### Finding All the Solutions of Trigonometric Equations

The mathematical solution explains how to solve the equation:

sin(x+150) = 1/√2 for x between 0? and 360?.

Graphical solutions show how a graphical calculator can be used to verify the solutions.

### Using Rcos(x + α) to Find the Maximum and Minimum Values of a Function and to Solve a Trigonometric Equation

The mathematical solution initially explains how to find the maximum and minimum values of f(x) = 5sin x + 2cos x and how to find, in radians to 2 decimal places, the smallest positive values of x at which they occur. f(x) is written in the form Rcos(x + α).

The second part of the explanation shows how the Rcos(x + α) form can be used to solve the equation 5sin x + 2cos x = 1.

Graphical solutions show how a graphical calculator can be used to verify the solutions.

### Trigonometry

These resources cover aspects of trigonometry suitable for students studying mathematics at A Level, as well as those students for whom mathematics is an integral part of their course. Some of the topics covered include the trigonometric ratios, using Pythagoras’ theorem, cosecant, secant and cotangent, the addition formulae , radians and trigonometric identities.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of trigonometry will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.

### Trigonometric Functions

This booklet aims to show the practical importance of trigonometric functions.

The booklet contains five case studies.

Cylindrical oil container covers applications of sine, cosine and tangent

Pipes covers use of Pythagoras' theorem and finding the length of an arc

Modelling hours of daylight applications of simple harmonic motion

Pull on the arms of a windsurfer resolving forces in equilibrium

Problems contains a variety of problems

The booklet is intended as enrichment material to be used in conjunction with a text book providing background theory and practice examples.