Remembering trigonometric values for common angles is a major problem. Here is a trick that can ease this task. It was told by our mathematics instructor in Matric (class X). He told that you will not find it in any book. He was right. I have not found it in any book. It is so useful and easy to remember. It is given below.
For example the value of or will be which is equivalent to or . Similarly the value of will be . For the values of ignore the denominator and divide the corresponding value of by the corresponding value of . For example to compute the value of , there is 3 written under and 1 written under . Therefore the value of will be . Similar reasoning can be applied to calculate the values for . The values for and can be calculated using their reciprocal relations.
The second formula is called reduction formula that I found in a mathematical handbook. It is given by
Or in terms of radian measure
any integer, positive, negative or zero.
any one of six trigonometric functions.
any real angle measure.
(i) If is even, then is the same function as .
(ii) If is odd, then is the co-function of . and , and , and and are co-functions of each other.
The second is determined by the quadrant in which angle or lies.
For example to calculate value of , we note that is multiplied by 3 which is odd. Therefore will be . The corresponding angle lies in 4th quadrant where the value of is negative. Thus we conclude that .
A pdf version of this post can be downloaded from here.