A Level Mathematics Syllabus Statement

Syllabus Content

Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Know and use exact values of sin, cos and tan for the following angles (in degrees and radians) 0°, 30°, 45°, 60°, 90°, 180° and multiples thereof

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Inverse Trig Calculator This calculator is designed to find all of the angles for a given trigonometric ratio and show them on a graph.

Common Trig Ratios Video You may not realise that it is possible to find sin60° or tan45° without a calculator. This video is to help you do the online, self-marking exercise.

Common Trig Ratios Degrees A self-marking exercise on finding the exact values of sine, cosine and tangent of special angles.

Common Trig Ratios Radians A self-marking exercise on finding the exact values of sine, cosine and tangent of special angles given in radians.

Here are some exam-style questions on this statement:

"Find the exact value of tan45° × sin30° × cos30°" ... more

"(a) Write down the exact value of \(\tan 60^o\)." ... more

"The area of triangle ABC (not drawn to scale) is " ... more

"The function \(f\) is defined by \(f(x) = \cos{ax} \) , where \(a > 0\). The following diagram shows part of the graph of \(f\), where x is in radians. There are local maxima at \(x = b , 2b \text{ and } 3b\)." ... more

"The diagram shows part of the graph of \(y=a\sin{(bx)}+c\) with a minimum at \((-2.5,-2)\) and a maximum at \((2.5,4)\)." ... more

"A Big Wheel at an amusement park has a diameter of length 70 metres which rotates at a constant speed. The bottom of the wheel is h metres above the ground. A seat starts at the bottom of the wheel.The wheel completes one revolution in 4 minutes. [The diagram is not to scale]" ... more

"(a) Sketch the graph of \(f(x) = 4\sin x - 5\cos x \), for \(–2\pi \le x \le 2\pi \)." ... more

"Consider a function \(f\), such that \(f(x)=7.2\sin(\frac{\pi}{6}x + 2) + b\) where \( 0\le x \le 12\)" ... more

"The height of water in metres above Chart Datum* in the Port of Bristol on a day in January is modelled by the function:" ... more

See all these questions

Here are some Advanced Starters on this statement:

Angle Thinking
Find the range of possible angles, x, for which tan x > cos x > sin x more

Cos 10 Equals p
Find the trigonometric values in terms of the given value, p. more

Tansum
Find the sum of the tangents of angles on a straight line. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Trigonometry Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Pupils begin by learning the names on the sides of a right-angled triangle relative to the angles. They then learn the ratios of the lengths of these sides and the connection these ratios have with the size of the angles. Having mastered right-angled triangle trigonometry pupils then progress to more advanced uses including the sine rule and cosine rules. The use of a scientific or graphing calculator is essential for this topic and correct, efficient use of the calculator is an important skill to develop. Here's a Trigonometry Wordsearch just for fun.

Furthermore

This video on Trig Graphs and Circular Functions is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course.

This video on Unit Circle and Trig Ratios is from Revision Village and is aimed at students taking the IB Maths AA SL and HL Standard level course

This video on Solving Trig Functions and Equations is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course.

Transum,

Saturday, August 17, 2019

"Here's an Advanced Lesson Starter that is just right to present to a class when they are learning exact values of common angles. It is a challenge to find the Tangent of 22.5^o without using a calculator but a helpful diagram is included."

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.