Question

How do you evaluate $\cos W=0.6157$?

Answer 1

Now we are given with $\cos W=1.6157$ . We will make use of the inverse function of cos to write another equation in ${{\cos }^{-1}}$ . Now we will find the value of cos inverse and hence find the value of W.

Complete step by step answer:
Now let us first understand the trigonometric functions and inverse trigonometric functions.
Trigonometric function are nothing but ratios of a right angle triangle,
Now the given function cos is ratio of adjacent side and hypotenuse in a right angle triangle.
Hence $\cos \theta$ gives us the value of the ratio for each angle $\theta$ .
Now for each trigonometric ratio we have its inverse trigonometric function.
Inverse function of any function is nothing but a function which nullifies the effect of the function. Let us understand this by an example.
If f is a function such that $f\left( x \right)=y$ then the function g is called the inverse function of f if $g\left( y \right)=x$ for all values of x and y.
Now the inverse function of cos is denoted by ${{\cos }^{-1}}x$ or arc cos .
Hence we can say that if $\cos \theta =x$ then ${{\cos }^{-1}}x=\theta$ .
Now we are given with an equation $\cos W=0.6157$ .
Hence we can say that ${{\cos }^{-1}}0.6517=W$ .
Now we calculating the value of ${{\cos }^{-1}}0.6517$ we get, ${{\cos }^{-1}}0.6157={{52}^{\circ }}$ .
Hence the value of W is ${{52}^{\circ }}$ .

Note:
Now note that the inverse function of f is generally denoted by ${{f}^{-1}}$ . The negative power is just a notation and should not be considered as a fraction. Hence we can say ${{f}^{-1}}\left( x \right)\ne \frac{1}{f\left( x \right)}$ . Also it should be noted that inverse function of all functions need not exist. The functions will have an inverse function only if the function is bijective.