Trigonometry

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Paul Howes

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Paul Howes 8 years, 6 months ago

Created this as a copy of Trigonometry.

Name	Status	Author	Last Modified
Trigonometry	Ready to use	Katie Lester	01/06/2016 09:47
Trigonometry	Ready to use	Jinhua Mathias	28/08/2024 12:15
LOOK AT OTHER TRIG QUESTIONS IN PREARRIVAL FOR UPDATED VERSIONS (this needs deleting)	Should not be used	Jinhua Mathias	28/08/2024 12:15
Trigonometry I: Right-angled triangles	Ready to use	Sarah Turner	30/08/2016 13:00
Trigonometry	draft	steve kilgallon	22/08/2017 16:18
FY001 EXAM 1 Trigonometry	draft	steve kilgallon	30/08/2016 15:14
Solucion triangulos rectangulos	draft	Marlon Arcila	19/09/2016 16:16
Solucion triangulos rectangulos	draft	Marlon Arcila	19/09/2016 16:47
Trigonometry	draft	Paul Howes	13/11/2016 18:20
Hannah's copy of Trigonometry	draft	Hannah Bartholomew	18/09/2017 15:09
Hannah's copy of Trigonometry I: Right-angled triangles	draft	Hannah Bartholomew	07/12/2016 11:24
Geometry: right-angled triangle	draft	Lovkush Agarwal	10/10/2018 10:56
Geometry. Right-angled triangle II. Version 1	Ready to use	Lovkush Agarwal	25/09/2019 09:42
Geometry. Right-angled triangle II. Version 2	Ready to use	Lovkush Agarwal	23/01/2019 17:25
Geometry. Right-angled triangle II. Version 3	Ready to use	Lovkush Agarwal	23/01/2019 17:25
Geometry. Right-angled triangle II. Version 4	Ready to use	Lovkush Agarwal	23/01/2019 17:25
Geometry. Right-angled triangle II. Version 5	Ready to use	Lovkush Agarwal	23/01/2019 17:25
Geometry. Right-angled triangle II. Version 6	Ready to use	Lovkush Agarwal	23/01/2019 17:25
Trigonometry	draft	Gareth Woods	02/07/2018 08:55
Kwame's copy of Trigonometry	draft	Kwame D Dwamena	15/03/2018 15:30
Trigonometry	draft	Mark Hodds	10/10/2018 09:03
David's copy of Trigonometry	draft	David Hudson	22/06/2018 01:37
Paul's copy of Trigonometry	draft	Paul Emanuel	28/06/2018 01:06
Brian's copy of Trigonometry	draft	Brian Walker	28/06/2018 01:07
Ralis's copy of Brian's copy of Trigonometry	draft	Ralis Vane-Tempest	28/06/2018 01:09
Diagnostic Test - Trigonometry	draft	Gareth Woods	04/07/2018 15:28
Geometry. Right-angled triangle. Lengths given, sin, cos, tan asked for	draft	Lovkush Agarwal	25/09/2019 09:34
cormac's copy of Trigonometry I: Right-angled triangles	draft	cormac breen	30/10/2018 16:11
Trigonometry: Right-angled triangle II. Version 6	draft	Clare Lundon	03/11/2018 23:33
Harry's copy of Trigonometry: Right-angled triangle II. Version 6	draft	Harry Flynn	15/11/2018 10:27
Diagnostic Test - Trigonometry	draft	Meetu Chhabra	21/05/2019 05:16
Maria's copy of Diagnostic Test - Trigonometry	draft	Maria Aneiros	29/05/2019 08:15
Michael's copy of Diagnostic Test - Trigonometry	draft	Michael Proudman	07/12/2021 11:53
Exam11 - Trigonometry	draft	Michael Proudman	07/12/2021 09:54
nuExam11 - Trigonometry	draft	Michael Proudman	07/12/2021 09:54
Aiping's copy of Geometry. Right-angled triangle II. Version 6	draft	Aiping Xu	27/06/2019 15:11
Aiping's copy of Geometry. Right-angled triangle II. Version 6	draft	Aiping Xu	27/06/2019 15:11
Aiping's copy of Geometry. Right-angled triangle II. Version 6	draft	Aiping Xu	27/06/2019 15:21
Right-angled triangle II	draft	Xiaodan Leng	10/07/2019 20:51
Right-angled triangle II	draft	Xiaodan Leng	10/07/2019 22:38
Trigonometry I: Right-angled triangles	draft	Xiaodan Leng	11/07/2019 05:37
Geometry. Right-angled triangle II. All versions	draft	Lovkush Agarwal	15/11/2019 16:47
Right Angle Trigonometry (missing side)	Ready to use	Andrew Chuter	06/04/2020 13:19
Musa's copy of 3 Right-angled triangles	draft	Musa Mammadov	27/06/2023 01:32
Cameron's copy of Right Angle Trigonometry (missing side)	draft	Cameron Ritchie	10/07/2020 03:19

There are 60 other versions that do you not have access to.

Question statement

Using the triangle pictured below (not to scale), find the specified side lengths using trigonometry and the given values.

Give your answer to two decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	[ 5, 7, 10, 9, 8, 4, 7 ]
x	list	[ 40, 60, 70, 50, 30, 25 ]
fa	integer	2
fh	integer	7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(3..10),7)

JME function reference

Description

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`

[ 5, 7, 10, 9, 8, 4, 7 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
1. Gap Number entry
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Part c) Gap-fill
1. Gap Number entry
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Part d) Gap-fill
1. Gap Number entry
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Part e) Gap-fill
1. Gap Number entry
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Part f) Gap-fill
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Gap-fill

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

$a=\var{a[0]}$

$x=\var{x[0]}^\circ$

$c=$ Unnamed gap

Advice

Each angle on a triangle is connected to two sides and is facing another.

The longest side of the triangle is always the hypotenuse.

The other side that makes the angle is called the adjacent.

The final side not connected in any way to the angle is called the opposite.

For example, using the image below, you can see which side is denoted by each term from the highlighted angle's perspective.

One of the ways you can approach this style of question is by using SOHCAHTOA.

This can be written more visually as

$\text{S}^\text{O}_\text{H}\space\text{C}^\text{A}_\text{H}\space\text{T}^\text{O}_\text{A}$

It represents each trigonometric function and what they are equivalent to.

Written out in full, we would have:

SIN: opposite / hypotenuse

COS: adjacent / hypotenuse

TAN: opposite / adjacent

For example, $\sin$ is represented by the first S.

If we were given an angle, say of $30^\circ$ ,

$\sin(30^\circ)=\frac{\text{opposite}}{\text{hypotenuse}}$

Evaluating $\sin(30^\circ)=\frac{1}{2}$ , we now know that $\frac{\text{opposite}}{\text{hypotenuse}}=\frac{1}{2}$

If we were given one of these sides, we would then be able to work out the other one by multiplying accordingly.

Similarly if we were given two sides, and told to work out a specific angle, we could.

Referring to the image above, suppose we want to find the highlighted angle and we are given that the hypotenuse is equal to $5$ units, and the adjacent is $4$ units.

We would determine from SOHCAHTOA that we need to use cos since we have the values for A and H.

So, $\cos(x)=\frac{4}{5}$

Hence, $x=\cos^{-1}(\frac{4}{5})=36.87^\circ$

Give a worked solution to the whole question.

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This question is used in the following exam:

FS0031 Maths CLE3 by Paul Howes in CLE3.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Paul Howes 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

$\text{S}^\text{O}_\text{H}\space\text{C}^\text{A}_\text{H}\space\text{T}^\text{O}_\text{A}$

Loading...

Error

Trigonometry

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Paul Howes 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

SOH CAH TOA\text{S}^\text{O}_\text{H}\space\text{C}^\text{A}_\text{H}\space\text{T}^\text{O}_\text{A}

Generated value: `list`

$\text{S}^\text{O}_\text{H}\space\text{C}^\text{A}_\text{H}\space\text{T}^\text{O}_\text{A}$