Group IIGroup II

We sometimes find it useful to remember the trigonometricratios for the angles

60 and45,30

These are easy to find using triangles.

In order to use the basic trig. ratios we need right angled triangles which also contain the required angles.

Consider an equilateral triangle.

Divide the triangle into 2 equal right angled triangles.

60 60

60 Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length.

22

2

( You’ll see why 2 is useful in a minute ).

Consider an equilateral triangle.

Divide the triangle into 2 equal right angled triangles.

60 60

30Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length.

1

22

2

We now consider just one of the triangles.

( You’ll see why 2 is useful in a minute ).

Consider an equilateral triangle.

Divide the triangle into 2 equal right angled triangles.

60

30Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length.

1

2

We now consider just one of the triangles.

( You’ll see why 2 is useful in a minute ).

1

2

From the triangle, we can now write down the trig ratios for 6030 and

Pythagoras’ theorem gives the 3rd side.3

60sin2

3 60cos 60tan2

1 3

30sin 30cos 30tan2

32

1

3

1

312 22

( Choosing 2 for the original side means we don’t have a fraction for the 2nd side )

60

30

1

1

45

45

211 22

2

45cos45sin 45tan2

11

For we again need a right angled triangle.

45

By making the triangle isosceles, there are 2 angles each of .45We let the equal sides have length 1.Using Pythagoras’ theorem, the 3rd side is

From the triangle, we can now write down the trig ratios for 45

2

1 45cos45sin 45tan 1

SUMMARY

60sin2

3 60cos 60tan2

13

30sin 30cos 30tan2

32

1

3

1

The trig. ratios for are: 6045,30 and

Ryan Gimena Barron Jay Fernandez Jerome Manila Jexy Gonzales Jaslyn Soriano

Special Thanks To:

Myk Kenneth Escala