Transcript Trigonometry cosine function grade B lesson

Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words. (Which
PLT skills?)
- Accurately use the cosine function to calculate missing
sides and angles in right angled triangles. (Grade B)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
BRAIN IN GEAR
Self
Manager
Team
Worker
Which ones are you using?
EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
SITPEPOO
Opposite
TANJACED
Adjacent
INES
Sine
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
Reflective
Learner
STARTER
Self
Manager
Team
Worker
Which ones are you using?
TASK
1)Write 0.1 as 2) Write 770000 in 3) Write
a fraction
1
=
10
=
standard form
5
7.7 x 10
=
18
20
4) Find 15% of $420
as a %
90%
=
$63
5)Write 0.00053 in 6) Expand and simplify: 7) Value of: 8) Value of:
standard -4form
= 5.3 x 10
EXTENSION
..
=
=
7(x + 2) - 3(x - 5)
7x + 14 – 3x + 15
4x + 29
0
=
89
1
=
4
32
5
2
Write 0.86 as a fraction
Factorise the following:
x = 0.868686…..
100x = 86.868686……
99x = 86
x2 - 11x + 30 = ( x - 6 )( x - 5 )
x
=
86
99
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
TRIGONOMETRY
Self
Manager
Team
Worker
Which ones are you using?
Make sure your calculator is set to D or Deg not R or Rad
INTRODUCTION – USING YOUR CALCULATOR
Find the values, rounding the answers to 3s.f.
where appropriate.
(a) sin 54 (b) sin 26 (c) sin 90 (d) sin 0
= 0
= 0.809
= 0.438
= 1
(e) cos 54 (f) cos 26 (g) cos 90 (h) cos 0
= 1
= 0.588
= 0.899
= 0
(i) tan 54 (j) tan 26 (k) tan 89 (l) tan 0
= 0
= 1.38
= 0.488
= 57.3
5
(p)
(n)
6
cos
24
(o) 8 tan 44
(m) 4 sin 62
sin 72
= 3.53
= 5.48
= 7.73
= 5.26
5
4
(q) 8
(r) 9
(s) sin-1 7 (t) cos-1 8
cos 35
= 9.77
tan 18
= 27.7
SHIFT sin
= 34.8
SHIFT cos
= 51.3
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
TRIGONOMETRY
Self
Manager
Which ones are you using?
INTRODUCTION – LABELLING SIDES CORRECTLY
This is
opposite
the
angle.
Team
Worker
This is
opposite the
right-angle.

This is next to the angle.
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
TRIGONOMETRY
INTRODUCTION – LABELLING SIDES CORRECTLY
Label the sides of the triangles below with opposite, adjacent and hypotenuse:
(b)
(d)
(a)
(c)
A
H
O
H
H
O O
A
A
A
(e)
O
(f)
A
H
A
O
H
O
A
(g)
H
(h)
A
H
O
O
H
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
COSINE FUNCTION
EXAMPLES
(a)
Which ones are you using?
H
θ
6cm A
Find the angle θ
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Adjacent
Hypotenuse
6
cos θ =
13 6
cos θ =
-1
Team
Worker
(b)
13cm H
O
Self
Manager
θ = cos 13
θ = 62.5°(3s.f)
16cm
O
57°
b A
Find the length of side b
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Adjacent
Hypotenuse
b
cos 57 =
16
cos θ =
b = 16 x cos 57
b = 8.71cm(3s.f)
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
COSINE FUNCTION
TASK (GRADE B)
(a) H
(b)
(c)
H
(d)
A
3m
A
A
(e)
(f)
H
A
H
Work out θ
Work out θ
Work out θ
(g)
H
A
Find the value of x
Work out θ
(h)
A
A
A
Find the value of x
H
H
Find the value of x
H
Find the value of x
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
COSINE FUNCTION
EXTENSION (GRADE B)
1) Angle θ has a cosine of
(a) H
(b)
. Calculate the missing lengths in these triangles.
H
(c)
(d)
H
A
A
x2 4
x2 10
A
x=4
2) Find the values of θ below:
(a)
(b)
H
A
x3 6
x3 15
H
x = 15
x10 20
x10 50 x
H
= 20
x6 12
x6 30
x = 30
(d)
H
(c) 0.56mA
3.27m
A
6m
0.5m
A
H
A
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
COSINE FUNCTION
Self
Manager
Which ones are you using?
MINI-PLENARY – SPOT THE MISTAKE
1) Find the angle θ
H
A
Team
Worker
2) Find the length of x
A
H
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
DISCOVERY
Self
Manager
Team
Worker
Which ones are you using?
LINK BACK TO OBJECTIVES
- Accurately use the sine function to
calculate missing sides and angles in right
angled triangles.
What grade
are we
working at?
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills
COSINE FUNCTION Which ones are you using?
PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B)
A window cleaner has a ladder which is 9m long. The window
cleaner leans it against a wall so that the foot of the ladder is 4m
from the wall. What angle does the ladder make with the ground?
Adjacent
Hypotenuse
cos θ = 4
9 4
cos θ =
9m
-1
θ = cos 9
θ = 63.6°(3s.f)
θ
4m
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about using the cosine
function to calculate missing sides and angles in right angled triangles. It can be a
skill or a reflection, or something else that might be prominent in your brain.
Where are we
in our
journey?
What grade
are we
working at?
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
www.mistrymaths.co.uk
I fully
understand
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
WWW (What Went Well)
EBI (Even Better If)
On your post it
notes…
Think about how you
can improve your
work.
www.mistrymaths.co.uk