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# Exact Trig Ratios

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by

## Mr Mattock

on 20 June 2016

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#### Transcript of Exact Trig Ratios

Exact Trig Ratios
Starter
Use Pythagoras' Theorem to find the missing lengths in these triangles. Leave your answers as square roots.
Exact Trig values table
0 30 45 60 90
Example
L.O. - Know some of the exact trig ratios and understand how to derive them.
1 cm
1 cm
2 cm
2 cm
2 cm
Starter
Use Pythagoras' Theorem to find the missing lengths in these triangles. Leave your answers as square roots.
1 cm
1 cm
2 cm
2 cm
2 cm
2
3
Exact trig values of 45 degrees
1 cm
1 cm
45
2
o
Write fractions that are equal to

(a) sin 45

(b) cos 45

(c) tan 45
Exact trig values of 45 degrees
1 cm
1 cm
45
2
o
Write fractions that are equal to

(a) sin 45 =

(b) cos 45 =

(c) tan 45 = 1
1
2
1
2
Exact Trig values of 30 and 60 degrees
2 cm
2 cm
2 cm
3
1 cm
2 cm
3
30
60
o
Write fractions that are the same as

sin 30

cos 30

tan 30

sin 60

cos 60

tan 60
Exact Trig values of 30 and 60 degrees
2 cm
2 cm
2 cm
3
1 cm
2 cm
3
30
60
o
Write fractions that are the same as

sin 30 =

cos 30 =

tan 30 =

sin 60 =

cos 60 =

tan 60 =
1
2
1
2
3
2
3
2
1
3
3
Sin

Cos

Tan
2
0
2
2
2
2
2
2
2
2
2
1
2
3
4
3
2
1
4
0
3
3
3
1
0
0
1
3
3
3
Example
tan 45 = 10/a
1 = 10/a so a = 10.

tan 30 = 10/b
1/ 3 = 10/b
3 = b/10
b = 10 3
a
b
c
c = a + b = 10 + (10 3 ) = 100 + 100x3 = 400
c = 400 = 20 metres
2
2
2
2
2
Example
sin 60 = 33/x

x
y
3 33
2 x
=
2 x
3 33
=
x =
66
3
sin 30 = 33/y

1 33
2 y
=
y
33
2 =
y = 66
y - x = 66 -
66
3
Example
Main Activity
Complete the Exact Trig values worksheet
Main Activity
Complete the Exact Trig values worksheet
1). 12 + 4 3 2). 12 + 12/ 3
3). 9 4). 9

5). base = 3 + 2 3, side = 3 3 - 2.
6). Perimeter = 6 + 3 6, area = 9 + 108
2
7). 16 + 16 3
8). 18 + 9 12
2
3
2
3
Activity