Transcript Trigonometry tangent function grade B lesson

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PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words. (Which
PLT skills?)
- Accurately use the tangent function to calculate
missing sides and angles in right angled triangles.
(Grade B)
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BRAIN IN GEAR
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EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
YOPSEHTENU
Hypotenuse
NOESCI
Cosine
TEATH
Theta
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
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STARTER
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TASK
1)Write 0.9 as 2) Write 690000 in 3) Write
a fraction
9
=
10
=
standard form
5
6.9 x 10
=
12
20
as a %
60%
4) Find 15% of $680
=
$102
5)Write 0.00026 in 6) Expand and simplify: 7) Value of: 8) Value of:
standard -4form
= 2.6 x 10
EXTENSION
..
=
=
5(x - 2) - 2(x - 5)
5x - 10 – 2x + 10
3x
Write 0.74 as a fraction
x = 0.747474…..
100x = 74.747474……
99x = 74
x
=
74
99
0
=
186
1
=
25
125
3
2
Factorise the following:
x2 + 2x - 35 = ( x + 7)( x - 5 )
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TRIGONOMETRY
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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) tan-1 7 (t) cos-1 8
cos 35
= 9.77
tan 18
= 27.7
SHIFT tan
= 29.7
SHIFT cos
= 51.3
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TRIGONOMETRY
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INTRODUCTION – LABELLING SIDES CORRECTLY
This is
opposite
the
angle.
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This is
opposite the
right-angle.

This is next to the angle.
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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
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TANGENT FUNCTION
EXAMPLES
(a)
O
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(b)
H
H
8cm
θ
64°
6cm A
11cm A
Find the angle θ
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Opposite
Adjacent
8
tan θ =
11 8
tan θ =
-1
θ = tan 11
θ = 36.0°(3s.f)
O
b
Find the length of side b
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Opposite
Adjacent
b
tan 64 =
6
tan θ =
b = 6 x tan 64
b = 12.3cm(3s.f)
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TANGENT FUNCTION
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TASK (GRADE B)
(a)
(b)
(c) A
O
O (d)
A
A
O
Work out θ
Work out θ
(e)
A
O
(f)
O
Work out θ
(g) A
Work out θ
O (h)
A
A
A
Find the value of x
O
Find the value of x
Find the value of x
O
Find the value of x
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TANGENT FUNCTION
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EXTENSION (GRADE B)
1) Angle θ has a tangent of
(a)
(b)
. Calculate the missing lengths in these triangles.
(c)
O
(d)
O
A
O
A
x=8
2) Find the values of θ below:
(a)
(b)
x4 16
x4 20
= 40
x8 32
x8 40
x = 40
(c)
A
3m
x10 40
x1050 x
x = 20
A
O (d)
5.27m
x2 8
x2 10
A
O
A
6m
O
A
16m
O
O
A
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TANGENT FUNCTION
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MINI-PLENARY – SPOT THE MISTAKE
1) Find the angle θ
2) Find the length of x
O
A
H
O
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DISCOVERY
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LINK BACK TO OBJECTIVES
- Accurately use the tangent function to
calculate missing sides and angles in right
angled triangles.
What grade
are we
working at?
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PLT Skills TANGENT FUNCTION Which ones are you using?
PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B)
A window cleaner leans his ladder against a wall so that the foot
of the ladder is 10m from the wall. The vertical length from the
ground to where the ladder rests against the wall is 8m. What
angle does the ladder make with the ground?
Opposite
Adjacent
tan θ = 8
10 8
tan θ =
8m
θ
10m
-1
θ = tan 10
θ = 38.7°(3s.f)
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about using the tangent
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.
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