Simon's copy of Trigonometry Cosine rule

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Simon Thomas 5 years, 11 months ago

Created this as a copy of Trigonometry Cosine rule.

Name	Status	Author	Last Modified
3 point triangle TestBed	draft	David Wishart	02/05/2017 22:00
3 point triangle	draft	David Wishart	31/03/2025 15:39
Ben's copy of 3 point triangle	draft	Ben Brawn	02/05/2017 05:21
3 side triangle	draft	David Wishart	07/05/2017 23:04
Right Angle triangle	draft	David Wishart	10/06/2017 22:53
Trigonometry Q2 Right angled triangle	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q3 Right angled triangle	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q4 Sine rule	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry Q5 Cosine rule	Ready to use	David Wishart	03/03/2020 15:15
Trigonometry to Find Missing Length	draft	Gareth Woods	21/07/2017 16:00
Trigonometry to Find Angle	draft	Gareth Woods	21/07/2017 16:02
Paul's copy of Trigonometry Q4 Sine rule	draft	Paul Hancock	05/09/2017 03:32
Question 4	draft	Paul Hancock	07/09/2017 01:42
Question 5	draft	Paul Hancock	05/09/2017 03:40
Right Triangle	draft	Paul Hancock	05/09/2017 03:57
MATH6058 Trigonometry Cosine rule	draft	Catherine Palmer	24/10/2017 11:06
Trigonometry Q1	Ready to use	David Wishart	05/06/2023 13:11
Kwame's copy of Paul's copy of Trigonometry Q4 Sine rule	draft	Kwame D Dwamena	15/03/2018 15:37
Kwame's copy of MATH6058 Trigonometry Cosine rule	draft	Kwame D Dwamena	15/03/2018 15:39
Trigonometry Application	draft	Mark Hodds	16/03/2018 09:35
Trigonometry Cosine rule	draft	Mark Hodds	16/03/2018 09:48
Trigonometry Sine rule	draft	Mark Hodds	16/03/2018 09:38
Trigonometry Sine rule	draft	Mark Hodds	16/03/2018 09:46
Christian's copy of Trigonometry Q1	draft	Christian Lawson-Perfect	13/06/2018 09:03
Network Demo	draft	Paul Hancock	04/07/2018 01:32
Sine, cosine, and area rules	draft	Sean Gardiner	17/02/2019 20:47
Sine, cosine, and area rules	draft	Sean Gardiner	13/02/2019 00:37
Right-triangle trigonometry	draft	Sean Gardiner	16/12/2018 21:58
Right-triangle trigonometry [OLD]	draft	Sean Gardiner	21/12/2021 03:15
Trigonometry Q3 (Right angled triangle)	draft	Michael Proudman	07/12/2021 10:48
Trigonometry to Find Missing Length (Right Angled Triangle)	draft	Michael Proudman	07/12/2021 10:48
Michael's copy of Trigonometry Q1	draft	Michael Proudman	07/12/2021 10:48
Michael's copy of Right-triangle trigonometry	draft	Michael Proudman	07/12/2021 10:48
Sine, cosine, and area rules (radians)	draft	Sean Gardiner	17/02/2019 20:47
SOHCAHTOA applied problem	Should not be used	Ruth Hand	12/07/2022 15:05
Simon's copy of Sine, cosine, and area rules	draft	Simon Thomas	02/05/2019 10:45
Simon's copy of Trigonometry Cosine rule	draft	Simon Thomas	02/05/2019 10:59
Meetu's copy of Michael's copy of Trigonometry Q1	draft	Meetu Chhabra	21/05/2019 05:14
Trigonometry Q1	draft	Meetu Chhabra	21/05/2019 05:15
Maria's copy of Sine, cosine, and area rules	draft	Maria Aneiros	24/05/2019 00:52
Maria's copy of Meetu's copy of Michael's copy of Trigonometry Q1	draft	Maria Aneiros	29/05/2019 08:19
Maria's copy of Trigonometry Q1	draft	Maria Aneiros	29/05/2019 07:52
Trigonometry: Sine Rule	draft	Xiaodan Leng	10/07/2019 22:55
Trigonometry Cosine rule	draft	Xiaodan Leng	10/07/2019 22:55
Right-triangle trigonometry	draft	Sean Gardiner	17/09/2020 23:54
Sine, cosine, and area rules	draft	Sean Gardiner	09/02/2020 22:14
Michael's copy of Right-triangle trigonometry	draft	Michael Proudman	07/12/2021 10:48
Pythagoras: calculating side length	Ready to use	Ruth Hand	08/03/2023 14:52
Right angled triangles: SOHCAHTOA 3 - random side or angle	Ready to use	Ruth Hand	27/09/2022 09:01
Right angled triangles: SOHCAHTOA 1 - find angle	Ready to use	Ruth Hand	27/09/2022 09:01
Right angled triangles: SOHCAHTOA 2 - find side	Ready to use	Ruth Hand	27/09/2022 09:01
GB1 Trigonometry - missing side	Ready to use	Megan Oliver	14/02/2025 14:31
GB6 Trigonometry - non-right angled trig	Ready to use	Oliver Spenceley	09/04/2024 17:51
GB2 Trigonometry - missing angle	Ready to use	Will Morgan	14/02/2025 14:29
GA2 Pythagoras - triangle	Ready to use	Will Morgan	09/04/2024 17:45

There are 172 other versions that do you not have access to.

Question statement

The cosine rule can be used to calculate angles and side lengths as follows:

Image result for cosine rule

This works for any triangle - it does not need to be right-angled.

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

unitList	list	[ "mm", "cm", "m", "km" ]
units	string	mm
a	integer	23
angleARough	integer	118
asinA	number	26.0491111658
angleMin	integer	30
angleBmax	integer	32
bMax	number	13.8039258229
bMin	number	13.0245555829
b	integer	13
angleBRough	number	29.9376533641
angleCRough	number	32.0623466359
c	number	14
angleA	number	116.7789415925
angleB	number	30.3047140565
angleC	number	32.916344351

Automatically regenerate variables?

Name

Data type

Value

(text strings)

Description

Units that are to be used for the question.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ "mm", "cm", "m", "km" ]

→ Used by:

units

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

{plotgraph(units,a,b,c,angleA,angleB,angleC)}

Use the cosine rule to calculate angles A, B and C correct to 2 d.p.

A = Gap 0. $^{\circ}$

B = Gap 1. $^{\circ}$

C = Gap 2. $^{\circ}$

Advice

We will use the cosine rule:

Image result for cosine rule

(a)

$a^2=b^2+c^2-2bc\cos A$

$\var{a}^2=\var{b}^2+\var{c}^2-2\times\var{b}\times\var{c}\cos A$

$\var{a^2}=\var{b^2+c^2}-\var{2*b*c}\cos A$

$\frac{\var{a^2}-\var{b^2+c^2}}{-\var{2*b*c}}=\cos A$

$A = \cos^{-1}(\frac{\var{a^2}-\var{b^2+c^2}}{-\var{2*b*c}}) = \var{angleA}$

(b)

$b^2=c^2+a^2-2ac\cos B$

$\var{b}^2=\var{c}^2+\var{a}^2-2\times\var{a}\times\var{c}\cos B$

$\var{b^2}=\var{c^2+a^2}-\var{2*a*c}\cos B$

$\frac{\var{b^2}-\var{a^2+c^2}}{-\var{2*a*c}}=\cos B$

$B = \cos^{-1}(\frac{\var{b^2}-\var{a^2+c^2}}{-\var{2*a*c}}) = \var{angleB}$

(c)

$c^2=b^2+a^2-2ba\cos C$

$\var{c}^2=\var{b}^2+\var{a}^2-2\times\var{b}\times\var{a}\cos C$

$\var{c^2}=\var{b^2+a^2}-\var{2*b*a}\cos C$

$\frac{\var{c^2}-\var{b^2+a^2}}{-\var{2*b*a}}=\cos C$

$C = \cos^{-1}(\frac{\var{c^2}-\var{b^2+a^2}}{-\var{2*b*a}}) = \var{angleC}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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This question is used in the following exam:

Trigonometry and Pythagoras by Simon Thomas in Maths support.

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Simon Thomas 5 years, 11 months ago

Error in variable testing condition

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Generated value: `list`

Parts

Gap-fill

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Simon's copy of Trigonometry Cosine rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`