Trigonometric Functions can be written in form of equations. These equations are dealt either on the basis of the Trigonometric Identities or the values of domains and ranges of functions. Mostly problems that are related to Trigonometry involve finding values of angles, domains, ranges, maximum and minimum values of the function etc. For example, suppose we have been given how to find sin a equals to 0.8?
In this equation we need to analyses the sine function. Its maximum value is 1 and minimum value is -1. So, one thing is clear that value of “a” lies between – 1800 and 1800. To evaluate the value of “a”, we multiply by the inverse of sine on both sides of function as:
Sin a = 0.8,
Or sin-1 sin a = sin-1 0.8
As we know that sin-1 sin a = a. We can write:
a = sin-1 0.8
Or a = 53.10
With help of given value of sine, we can find out the other Trigonometric Functions as follows:
Given, sin a = 0.8,
Or sin a = 4 / 5,
In Right Triangle we have: Hypotenuse = 5 and perpendicular = 4.
So, the base would be: b2 = 52 – 42 = 25 – 16 = 9,
Or b = 3,
So, cos a = 3 / 5, tan a = 4 / 3, cot a = 3 / 4, cosec a = 5 / 4 and sec a = 5 / 3,
If we evaluate the value of angle using any of the trigonometric function, we would get the same value 53.10 of angle between two shorter legs of right – angled triangle. Same procedure of taking inverse will be used.