Basic trigonometry

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AJAY OTTA 4 years, 11 months ago

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Question statement

Fill in the gap.

Give any introductory information the student needs.

			Name	Type	Generated Value

triplet	list	[ 16, 63, 65 ]
a	integer	-16
b	integer	-63
c	integer	65

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random([[3,4,5],[5,12,13],[7,24,25],[8,15,17],[9,40,41],[11,60,61],[12,35,37],[16,63,65],[20,21,29],[20,99,101]])
​

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`

[ 16, 63, 65 ]

→ Used by:

"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value
"Part b)" → "Unnamed gap" - Minimum accepted value
"Part b)" → "Unnamed gap" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

The maximum of $(\var{a})\cos\theta +(\var{b})\sin\theta$ =Unnamed gap

Advice

if we write $\boxed{\var{a}=r\sin\alpha}$ and $\boxed{\var{b}=r\cos\alpha}$ for some $r$ and $\alpha$ then we have $(\var{a})\cos\theta+(\var{b})\sin\theta=(r\sin\alpha)\cos\theta+(r\cos\alpha)\sin\theta=r\sin(\alpha+\theta)$ . Then the maximum and minimum value will be $r$ and $-r$ since $-1\leq\sin(\alpha+\theta)\leq 1$

To find $r$ we do the following: $r^2\sin^2\alpha=(\var{a})^2$ and $r^2\cos^2\alpha=(\var{b})^2 \implies r^2\sin^2\alpha+r^2\cos^2\alpha=(\var{a})^2+(\var{b})^2\implies r^2(\sin^2\alpha+\cos^2\alpha)=(\var{a})^2+(\var{b})^2\implies r^2=(\var{a})^2+(\var{b})^2\\ \implies r=\sqrt{({\var{a})^2+(\var{b})^2}}=\var{c}$

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Summer Bridge Course by AJAY OTTA in Koutilya.

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Taxonomy: mathcentre

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Taxonomy: Context

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AJAY OTTA 4 years, 11 months ago

AJAY OTTA 5 years, 1 month ago

AJAY OTTA 5 years, 1 month ago

Error in variable testing condition

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Generated value: `list`

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Basic trigonometry

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

AJAY OTTA 4 years, 11 months ago

AJAY OTTA 5 years, 1 month ago

AJAY OTTA 5 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`