Trig Equation Basics (cos)

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Mike Phipps

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Mike Phipps

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Ready to use

3 years, 5 months ago

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Mike Phipps 3 years, 5 months ago

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Mike Phipps 3 years, 5 months ago

Gave some feedback: Ready to use

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Mike Phipps 3 years, 6 months ago

Created this as a copy of Trig Equation Basics (sin).

Name	Status	Author	Last Modified
Trig Equation Basics (tan)	Ready to use	Mike Phipps	03/11/2021 16:45
Trig Equation Basics (sin)	Ready to use	Mike Phipps	03/11/2021 16:45
Trig Equation Basics (cos)	Ready to use	Mike Phipps	03/11/2021 16:45

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Question statement

Simpler Trig Questions

Give any introductory information the student needs.

			Name	Type	Generated Value

coeffsin	integer	5
RHS	integer	1
val_sin	rational	1/5
second_soln	decimal	dec("1.6846304096718451143414955842416353386e+2")
first_soln	decimal	dec("1.153695903281548856585044157583646613999e+1")
first_soln_3	string	11.5
second_soln_3	string	168
first_soln_5	string	11.537

			Name	Type	Generated Value

a	integer	20
b	integer	3
c	integer	6
cosx	rational	3/20
x_1_3sf	string	1.42
x_2_3sf	string	4.86
x_3_3sf	string	7.70
x_1	decimal	dec("1.420228054018210592808061390172356051624")
x_2	decimal	dec("4.862957253161375407191938609827643948376")
x_3	decimal	dec("7.703413361197796592808061390172356051624")
x_1_6sf	string	1.42023

			Name	Type	Generated Value

t	number	-2.7
t_1	number	-1.2160906748
t_2	number	1.9255019788
t_1_5sf	string	-1.2161
t_1_3sf	string	-1.22
t_2_3sf	string	1.93

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `integer`

→ Used by:

val_sin

This variable doesn't seem to be used anywhere.

Parts

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1. Gap x1 Number entry
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2. Gap x2 Number entry
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3. Gap x3 Number entry
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Ask the student a question, and give any hints about how they should answer this part.

Solve $\simplify{{a}cos(x)+{b}}=\var{c}$ between $0<x<3 \pi$

Write your answers below in ascending order and to 3 significant figures.

$x=$ x1 $^c$ or x2 $^c$ or x3 $^c$

Advice

WORKED SOLUTIONS

$\begin{align} \simplify{{a}cos(x)+{b}}&=\var{c} \\\\ cos{x}&=\frac{\var{c}-\var{b}}{\var{a}} \\\\ x &=cos^{-1}\frac{\simplify{{c}-{b}}}{\var{a}} \\\\ x_1 &=\var{x_1_3sf}^c \text { to 3 sig fig} \\\\ x_2 &=2\pi-\var{x_1_6sf}=\var{x_2_3sf}^c\text { to 3 sig fig} \\\\ x_3&=\var{x_1_6sf}+2\pi=\var{x_3_3sf}^c\text { to 3 sig fig} \end{align}$

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This question is used in the following exams:

Trigonometry by Mike Phipps in Intro Maths.
Trigonometry by Dr Palat Meethale Ushasree in Dr Palat Meethale's workspace.
Trigonometry Exam by Michael O'Connor in Glasgow Numbas Question Pool.

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Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Trig Equation Basics (cos)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`