T-ratios of standard angles
0o, 30o, 45o, 60o and 90o are called standard angles.These angles are called standard angles because it is possible to obtain simple mathematical ratios for these angles.
The students are advised to learn the T-ratios of these angles, they can also obtain them as shown in the derivation.T-ratios of 45o
Let 
\ AB = BC = a
Using Pythagoras TheoremAC2 = a2 + a2 = 2a2




T-ratios of 30o and 60o
Let
and 
In 30o - 60o - 90o triangle, it can be proved that the hypotenuse is double the side opposite to 30o (see proof in Geometry Section),
AC = 2ABLet AB = a
AC = 2a
Using Pythagoras Theorem
BC2 = (2a)2 - a2= 4a2 - a2
= 3a2



T-ratios of 0o and 90o
Draw a circle with radius r and XOX' and YOY' as axes.
Let 
Let 

We observe A"B" > A'B' > AB, denominator remains 'r' (radius).
As the angle increases sine ratio increases.

As the angle increases cosine ratio decreases,
When a = 0,

When 

(infinity)

(i) 
(iii) 
Aid to Memory

Aid to memorise the table for standard angles:
(a) Write 0, 1, 2, 3, 4 over each column as shown above.
(b) Divide each number by 4 and take the square root. The values obtained are sine ratios.(c) Write these ratios in reverse order and you obtain the cosine ratios
(sin A = cos B if A + B = 90o)(d) Divide each sine ratio by cosine ratio and you obtain the values of corresponding tangent ratios





= sin 60
R.H.S 2 sin A cos A = 2 sin 30 cos 30

sin 2A = 2 sin A cos A
Hence L.H.S. = R.H.S.
