**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**

Answers

Answers

**Key**

Examples

Examples

**Activities**