Values of Trigonometric ratios for 0, 30,45, 60 and 90 degrees
I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0, 30, 45, 60 and 90. These values are used very often and it is recommended from my point of view that student should be able to tell the values instantly when asked.
There is a proper method to memorize all of them. Lets go through it.
In this post our motive is to learn how to fill the table. Once, you learn to fill this table, you would be able to calculate any value in your mind.
Just memorize the values for sin 0, sin 30, sin 45, sin 60 and sin 90. Even there is no need to try too hard to memorize them. There is an easy way to memorize them.
Note down the pattern from sin 0 to sin 90:
Hence, we can now fill all sin values in the table.
Now, we will fill all the cos values.
All the cos values are filled in opposite order starting from sin 0 to sin 90. I mean to say that
sin 0 = cos 90
sin 30 = cos 60
sin 45 = cos 45
sin60 = cos 30
sin 90 = cos 0
Hence, all the cos values can be filled now.
We know that tan = (sin )/(cos )
Hence, all the tan values can be obtained from sin and cos values.
tan 0 = sin 0 / cos 0 = 0/1 = 0
tan 30 = sin 30 / cos 30
tan 45 = sin 45 / cos 45
tan 60 = sin 60 / cos 60
tan 90 = sin 90 / cos 90 = 1/0 which is NOT DEFINED
Similarly, we have sec = 1/cos , cot = cos / sin and cosec = 1/ sin .
Hence, all the tan, sec, cosec and cot values can be filled now.
Now, try to derive these values in your mind :).