Transcript Slide 1

Further
Trigonometry
Learning Outcomes




Calculate distances and angles in solids using plane sections
and trig ratios
Be able to sketch graphs of sine, cosine and tangent functions
Use sine (including the ambiguous case) and cosine rules to
solve problems, including simple cases in 3D
Be able to use ½absinC to calculate the area of a triangle
Further Trig
Pythagoras’ Theorem
& 3D Trig
Consider the cuboid below
Find:
i. The length of the diagonal DG
ii. The length of the diagonal FD
iii. The angle the line FD makes with the
base DCGH
Revision of Trig &
Pythagoras
Further Trig
Find x on the following right angled triangles.
1.
x
4
4.
5
6.
4
x
25º
30º
10
3
x
x
10
x
5.
x
10
5
7
15
3.
2.
7.
3
x
7.5
3.2
Sine Rule
Further Trig
B
a
c
A
For a side
For an angle
b
C
a  b  c
sin A sin B sin C
sin A  sin B  sin C
a
c
b
Sine Rule
Further Trig
Find angle C.
B
A
8
9
50º
?
b
C
Sine Rule
Further Trig
Find the length of AC.
A
62º
B
76º
?
9
42º
C
Cosine Rule
Further Trig
Use with non right angled triangles
B
a
c
A
b
C
a2 = b2 + c2 – 2bc cos A
Cosine Rule
Further Trig
A
105º
8.1
5.2
C
x
B
B
11.4
4.8
x
A
8.5
C
Further Trig
Additional Notes
Further
Trigonometry
Learning Outcomes:
At the end of the topic I will be able to




Can
Do
Revise
Further




Use sine (including the ambiguous case) and cosine
rules to solve problems, including simple cases in 3D


Be able to use ½absinC to calculate the area of a
triangle


Calculate distances and angles in solids using plane
sections and trig ratios
Be able to sketch graphs of sine, cosine and tangent
functions