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- 3.1 Three Dimensions.
- 3.7 Circular Functions.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Trigonometry in 3D Calculate the lengths of sides and the size of angles in three dimensional shapes.
- Volume Video There are simple formulas that can be used to find the volumes of basic three-dimensional shapes.
- Volume Use formulae to solve problems involving the volumes of cuboids, cones, pyramids, prisms and composite solids.
- 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
- Cylinders Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions
- Surface Area Video Finding the surface are of three dimensional shapes can involve some interesting formulae.
- Inverse Trig Calculator This calculator is designed to find all of the angles for a given trigonometric ratio and show them on a graph.
- Three Dimensional Trigonometry Video When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.
- Surface Area Work out the surface areas of common solid shapes in this collection of exercises.

Here are some exam-style questions on this topic:

- "
*Twenty four spherical shaped chocolates are arranged in a box in four rows and six columns.*" ... more - "
*Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH.*" ... more - "
*The diagram shows a rectangular-based pyramid, TABCD (not drawn to scale).*" ... more - "
*ABC is a triangular car park on horizontal ground. The length of AB is 90m and the length of AC is 65m. The size of angle BCA is 68*" ... more^{o}. - "
*Consider the graph of \(f(x)=a\sin(b(x+c))+12\), for \(0\le x\le 24\).*" ... more - "
*A metal sphere has a radius 7.2 cm.*" ... 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 solid metal cylinder has a base radius of 5cm and a height of 9cm.*" ... more - "
*The Big Wheel at Fantasy Fun Fayre rotates clockwise at a constant speed completing 15 rotations every hour. The wheel has a diameter of 90 metres and the bottom of the wheel is 6 metres above the ground.*" ... more - "
*The population of sheep on a ranch is modelled by the function \(P(t)= 65 \sin(0.4t-3.2)+450\), where t is in months, and \(t=1\) corresponds to 1st January 2015.*" ... more - "
*A wedge is to be cut from a log in the shape of a cylinder as shown in the diagram below (not to scale).*" ... more - "
*The Fun Wheel at the Meller Theme Park rotates at a constant speed.*" ... more - "
*(a) Sketch the graph of \(f(x) = 4\sin x - 5\cos x \), for \(–2\pi \le x \le 2\pi \).*" ... more - "
*Let \(f(x)=\sin ( \frac {\pi}{4}x) + \cos ( \frac {\pi}{4}x) \), for \(-4\le x \le 4\)*" ... 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 above the ground, H metres, of a passenger on a Ferris wheel t minutes after the wheel starts turning, is modelled by the following equation:*" ... more

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**Cuboid**

Find the dimensions of a cuboid matching the description given 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.

- Shape (3D) A particular skill is required to be able to excel in this area of Mathematics. Spatial awareness is important for solving multi-step problems that arise in areas such as architecture, engineering, science, art, games, and everyday life. Children have varying abilities visualizing three dimensional relationships but these abilities can be developed through practical activities and working through mathematical problems. Breaking down three dimensional situations into smaller two dimensional parts in an important strategy for problem solving. See also the "Shape" Starters.
- 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.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.