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.

Table 1: Common trigonometric values
Table 1: Common trigonometric values

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.


Example
Example

Consider the image on the right.

Let's say b = 4 and Θ = 300and 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/cosΘ = 4/cos(300) = 4/(√3/2)

c = 4.62(approx)

Similarly,

tanΘ = a/b

So, a = b*tanΘ = 4*tan(300) = 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,

c2 = a2 + b2

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:

c2 = c2*sin2Θ + c2*cos2Θ

c2=c2*(sin2Θ + cos2Θ)

Thus, we prove

sin2Θ + cos2Θ = 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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