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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 = 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)
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,
Also, sinΘ= a/c. Hence,
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.