Question

How do you solve the equation \[\tan G = 0.125\]?

Answer 1

Hint: According to the question we have to determine the solution of the equation\[\tan G = 0.125\]. So, to determine the solution of the given trigonometric equation first of all we have to assume that the given equation is asking us to solve for the G. So, we have to solve the given equation for G.
Now, we have to use the inverse function of tan we can also understand about the inverse function as explained below:
Inverse function: Inverse function is the function that reverses the other given function and if the function is applied to an input a which gives the result as y. Then applying its reverse function gives the result x which is g(y) = x.
We can also called the given trigonometric function as$\arctan $or ${\tan ^{ - 1}}$
Now, to solve the given trigonometric function we have to take the inverse function of the both sides of the given equation.
Now, we will obtain a primary solution for G and as we know that there are other values of G that will satisfy the given equation.

Complete step by step solution:
Step 1: First of all we have to assume that the given equation is asking us to solve for the G. So, we have to solve the given equation for G. Which is mentioned in the solution hint.
Step 2: Now, to solve the given trigonometric function we have to take the inverse function of the both sides of the given equation. Hence,
$ \Rightarrow \arctan (\tan G) = \arctan (0.125)$
Step 3: Now, with the help of the trigonometric expression as obtained in the solution step 2 we have to determine the value of G which is as determined below.
$ \Rightarrow G = \arctan (0.125) \cong 0.124$ radians
Step 4: Now, we will obtain a primary solution for G and as we know that there are other values of G that will satisfy the given equation. Hence,
$ \Rightarrow G \cong 0.124 + n.\pi $, where n belongs to Z.

Hence, we have determined the solution of equation \[\tan G = 0.125\] which is $ \Rightarrow G \cong 0.124 + n.\pi $, where n belongs to Z.

Note:
It is necessary that we have to let that equation be asked to solve for G and for that we can use the inverse to find the inverse of the given equation which is in the form of trigonometric function.
Function that reverses the other given function and if the function let f applied to an input a which gives the result as y. Then applying its reverse function gives the result x which is g(y) = x.