Download Trigonometry

Yr 10 Unit 8 –Algebra – Higher - Trigonometry
5 lessons
Support Objectives
Grade
Ref
Grade
B
Ref
H3.2g
B
H3.2g
A
H3.2g
A
H3.2g
A
H2.6f
A
H3.2g
A
H3.2g
A
H3.2g
Grade
A*
Ref
H3.2g
1
2
Core Objectives
1 Use sine, cosine and tangent to calculate a side in a right-angled
triangle.
AQA Higher book II pages 232 – 234
PPT Trigonometry introduction
FVT Trigonometry
ET Non calculator trigonometry
Trigonometry exam questions
2 Use sine, cosine and tangent to calculate an angle in a right-
angled triangle.
AQA Higher book II pages 235 – 237
FVT Trigonometry
Trigonometry exam questions
3 Use trigonometry to find sides and angles in three dimensions.
AQA Higher book II pages 238 – 239
Starter – 3D Trigonometry
3D Problems – exam questions
4 Find the angle between a line and a plane.
AQA Higher book II pages 238 -239
5 Sketch and draw trigonometric graphs.
AQA Higher book II pages 241 – 243
FVT Trig graphs
6 Use the sine rule to find the missing sides and angles in any
triangle.
AQA Higher book II pages 246 – 248
Starter – sine and cosine rule
Sine and cosine rule exam questions
7 Use the cosine rule to find the missing sides and angles in any
triangle.
AQA Higher book II pages 251 – 253
Starter – sine and cosine rule
Sine and cosine rule exam questions
8 Use the formula for the area of a non right-angled triangle.
AQA Higher book II pages 255 – 256
Starter – area of a triangle trig
Extension Objectives
1 Understand the graphs of trigonometric functions for angles of
any size.
AQA Higher book II pages 241 - 243
Student Self Assessment Sheet
Objectives
Grade
1
2
3
4
5
6
7
8
9
Use sine, cosine and tangent to calculate a side in a
right-angled triangle.
Use sine, cosine and tangent to calculate an angle in
a right-angled triangle.
Use trigonometry to find sides and angles in three
dimensions.
Find the angle between a line and a plane.
Sketch and draw trigonometric graphs.
Use the sine rule to find the missing sides and
angles in any triangle.
Use the cosine rule to find the missing sides and
angles in any triangle.
Use the formula for the area of a non right-angled
triangle.
Understand the graphs of trigonometric functions
for angles of any size.
Vocabulary
Trigonometry
Tangent (tan)
Isosceles triangle
Hypotenuse
Sine (sin)
Opposite side
Adjacent side
Angle of elevation
  
B
B
A
A
A
A
A
A
A*
Cosine (cos)
Angle of depression
Bearing
Trigonometric functions
Ideas for starters
1) Students draw a 6cm by 2cm rectangle and measure the length of the diagonal. Predict the
length of a 12cm by 4cm rectangle, a 3cm by 1cm rectangle etc. Draw them to check.
2) Rest a metre rule against a wall and measure the angle of elevation and the height the
ruler reaches up the wall. E.g assume the angle is 620 and the height is 0.88m. If you keep
the angle at 620, how far up the wall would: a 2m rule reach? A 5 metre ladder reach? A 10cm
pencil reach? Etc Establish that 0.88 is linked to 620.
3) Students draw 4 different rectangles where length = 2 x width. Students measure the
angle between the length and the diagonal. Discuss why all answers are about 26.50.
4) Identify all the right angles in a cube.
5) Practice squares and square roots. How many Pythagorean triples can you find in 5
minutes?
6) A wheel has a radius of 1m. A spot of paint is on the rim immediately to the right of the
centre. What is the height of the spot above the centre when the wheel has turned 10 0
anticlockwise?
7) When does sin x = cos x? When does sin x = tan x? When does cos x = tan x?
8) Discuss the differences between the sine rule and cosine rule and when they are used.
9) Write definitions for: isosceles, bearing, sine, cosine, tangent, opposite side, adjacent
side, hypotenuse, Pythagoras’ Theorem.
10) How do you find the area of a triangle?
HOLS/maths investigations
Use of spaghetti and jelly babies to construct 3D shapes and calculate lengths and angles.
ICT links / citizenship
Use of omnigraph to understand and investigate trigonometric graphs
Ideas for plenaries
1) Why is sin 30 = 0.5? (Consider an equilateral triangle split into two identical halves). Use
Pythagoras for sin 60 and sin 45.
2) Invent a pneumonic to help remember the trigonometric ratios.
3) Which is the larger angle? The one between the body diagonal of a cube and its base or
the one between the diagonal of a 2 x 1 rectangle and the length?
4) What is the greatest value of sinx, cosx and tanx. Explain your answer. What are the
minimum values?
5) Present a display of trig graphs and ask the students what their equations could be.
6) Discuss with the students where sine and cosine functions appear in nature and in real life.
7) Discuss when to use the sine rule and when to use the cosine rule.
8) An equilateral triangle has an area of 20cm2. Find the length of each side.
Ideas for homework
1) AQA Higher homework book II pages 91 – 93 homework 1.
2) AQA Higher homework book II pages 93 - 94 homework 2.
3) AQA Higher homework book II pages 94 - 95 homework 3.
4) AQA Higher homework book II pages 95 - 97 homework 4.
5) AQA Higher homework book II pages 97 - 98 homework 5.
6) AQA Higher homework book II pages 99 - 100 homework 6.
7) AQA Higher homework book II pages 101 - 102 homework 7.
Webmaths – trigonometry angles
Webmaths – trigonometry sides
Ideas for Formative Comments