Transcript Trigonometry sine function grade B lesson

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LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words. (Which
PLT skills?)
- Accurately use the sine 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:
NEVERIS
Inverse
TAHET
Theta
TOPHEYESUN
Hypotenuse
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
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STARTER
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TASK
1)Write 0.7 as 2) Write 68000 in 3) Write
a fraction
7
=
10
=
5)Write 0.0081 in
standard -3form
= 8.1 x 10
EXTENSION
..
standard form
4
6.8 x 10
=
18
25
4) Find 15% of $220
as a %
72%
=
$33
6) Expand and simplify: 7) Value of: 8) Value of:
=
=
6(x + 1) - 3(x - 4)
6x + 6 – 3x + 12
3x + 18
3
2
0
=
66
1
=
100
1000
Write 0.79 as a fraction
Factorise the following:
x = 0.797979…..
100x = 79.797979……
99x = 79
x2 - 9x + 14 = ( x - 7 )( x - 2 )
x
=
79
99
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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) sin-1 7 (t) cos-1 8
cos 35
= 9.77
tan 18
= 27.7
SHIFT sin
= 34.8
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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SINE FUNCTION
EXAMPLES
(a)
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H
θ
A
Find the angle θ
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Opposite
Hypotenuse
4
sin θ =
11 4
sin θ =
-1
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(b)
11cm H
O 4cm
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θ = sin 11
θ = 21.3°(3s.f)
14cm
b O
42°
A
Find the length of side b
SUBSTITUTE
IN
THE
VALUES
LABEL
SIDES
WRITE
DOWNTHE
THE
FORMULA
Opposite
Hypotenuse
b
sin 42 =
14
sin θ =
b = 14 x sin 42
b = 9.37cm(3s.f)
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SINE FUNCTION
TASK (GRADE B)
(a)
(b)
H
O
O
Work out θ
(f)
H
H
O
Work out θ
(g)
H
(d)
H
O
Work out θ
(e)
(c)
H
Work out θ
O
(h)
H
O
Find the value of x
O
Find the value of x
H
Find the value of x
O
Find the value of x
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SINE FUNCTION
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EXTENSION (GRADE B)
1) Angle θ has a sine of . Calculate the missing lengths in these triangles.
(a)
(b)
(c)
(d)
H
H
O
O
H
O
x2 6
x2 10
x=6
2) Find the values of θ below:
(a)
(b)
H
O
O
H
x3 9
x3 15
x = 15
H
x10 30
x10 50 x
x6 18
x6 30
= 30
x = 30
(d)
H
O
(c)
0.12m
5m
0.5m
O
H
O
6.5m
64.5
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SINE FUNCTION
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MINI-PLENARY – SPOT THE MISTAKE
1) Find the angle θ
2) Find the length of x
H
O
H
O
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DISCOVERY
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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?
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SINE FUNCTION
PLENARY ACTIVITY– PRACTICAL PROBLEM (GRADE B)
A window cleaner has a ladder which is 7m long. The window
cleaner leans it against a wall so that the foot of the ladder is 3m
from the wall. What angle does the ladder make with the wall?
θ
7m
Opposite
Hypotenuse
sin θ = 3
7 3
sin θ =
θ = sin
-1
7
θ = 25.4°(3s.f)
3m
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about using the sine
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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