**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.**

**(i)**

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.

sin 0

sin 30

sin 45

sin 60

sin 90

**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 :).