Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees

 

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^\circ, 30^\circ, 45^\circ, 60^\circ and 90^\circ. 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.

 

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

(i)

Just memorize the values for sin 0^\circ, sin 30^\circ, sin 45^\circ, sin 60^\circ and sin 90^\circ. Even there is no need to try too hard to memorize them. There is an easy way to memorize them.

 

sin 0^\circ=\sqrt{\frac{0}{4}}=0

 

sin 30^\circ=\sqrt{\frac{1}{4}}=\frac{1}{2}

 

sin 45^\circ=\sqrt{\frac{2}{4}}=\frac{1}{\sqrt{2}}

 

sin 60^\circ=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}

 

sin 90^\circ=\sqrt{\frac{4}{4}}=1

 

Note down the pattern from sin 0^\circ to sin 90^\circ:

\sqrt{\frac{0}{4}},\sqrt{\frac{1}{4}}, \sqrt{\frac{2}{4}}, \sqrt{\frac{3}{4}}, \frac{\sqrt{4}}{4}

 

Hence, we can now fill all sin values in the table.

 

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

Now, we will fill all the cos values.

All the cos values are filled in opposite order starting from sin 0^\circ to sin 90^\circ. I mean to say that

 

sin 0^\circ = cos 90^\circ

 

sin 30^\circ = cos 60^\circ

 

sin 45^\circ = cos 45^\circ

 

sin60^\circ = cos 30^\circ

 

sin 90^\circ = cos 0^\circ

 

Hence, all the cos values can be filled now.

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

We know that tan \theta = (sin \theta)/(cos \theta)

Hence, all the tan values can be obtained from sin and cos values.

 

tan 0^\circ = sin 0^\circ / cos 0^\circ = 0/1 = 0

 

tan 30^\circ = sin 30^\circ / cos 30^\circ=\frac{1}{\sqrt{3}}

 

tan 45^\circ = sin 45^\circ / cos 45^\circ=1

 

tan 60^\circ = sin 60^\circ / cos 60^\circ=\sqrt{3}

 

tan 90^\circ = sin 90^\circ / cos 90^\circ = 1/0 which is NOT DEFINED

 

Similarly, we have sec \theta = 1/cos \theta, cot \theta = cos \theta / sin \theta and cosec \theta = 1/ sin \theta.

 

Hence, all the tan, sec, cosec and cot values can be filled now.

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

Now, try to derive these values in your mind :).


 

27 Responses to “Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees”

Leave a Reply