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.