# Learn Basic Trigonometry Table : Help in Easily Learning Simple Trig Math - Part 2

In the previous hub, we have seen a rhyme which we can use to memorize the basic trigonometric equations. Now we will take a look at some of the common trigonometric values and examples.

The table below shows some of the common trigonometric values. We can see that cos Θ has the same sequence as that of sin Θ but in reverse order.

In the case of tan Θ, the equation is

tan Θ = sin Θ / cos Θ

Thus, all the values given in the table 1. for tan Θ, for a given Θ, can be calculated by dividing the sin Θ by cos Θ for the same Θ.

Consider the image on the right.

Let's say **b = 4 **and **Θ = 30 ^{0}**and the angle between

**a**and

**b**is right angle.

From the equations, we have from Part 1 of the hub's series:

**cosΘ = b/c**

So,** c = b/cos****Θ = 4/cos(30 ^{0}) = 4/(√3/2)**

**c = 4.62(approx)**

Similarly,

**tanΘ = a/b **

**So, a = b*tan****Θ = 4*tan(30 ^{0}) = 4*(1/√3)**

**a = 2.31(approx)**

**Proving sin2Θ + cos2Θ = 1 : **

Consider Figure 1, once again. It's a right-angled triangle. We know, from Pythagorean theorem, that, square of the hypotenuse is the sum of the square of the other two sides, that is,

**c ^{2} = a^{2} + b^{2}**

Now, we know that, cosΘ=b/c. Therefore,

**b=c*cosΘ**

Also, sinΘ= a/c. Hence,

**a=c*sinΘ**

Therefore, from the above two equations and the Pythagorean equation, we have:

**c ^{2} = c^{2}*sin^{2}Θ + c^{2}*cos^{2}Θ**

**c2=c ^{2}*(sin^{2}Θ + cos^{2}Θ)**

Thus, we prove

**sin ^{2}Θ + cos^{2}Θ = 1**

In the next hub, we will prove similar trigonometric relations.

**This article is Part 2 of the series of articles related to Learning Trigonometry. Read the other part/s for more information.**

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