Question

How do you find the exact value of \[\cos (\theta )\cos (\theta )\] ?

Answer 1

Hint: To find the exact value of the trigonometric function we have to solve the given function for value which is asked for, that is you have to solve for the angle which satisfies the given value. For that we have to take the inverse of the function, for that we have to transfer the trigonometric function to the right side of the equation and then for the given value we can find the value of angle.

Complete step by step solution:
The given question is to find the value of \[\cos (\theta )\cos (\theta )\]. Here we have to assume a value say “x” for which we are going to find the value of the given function, let’s make the expression with the assumed value, on solving we get:
\[ \Rightarrow \cos (\theta )\cos (\theta ) = x\]
Now here we can solve the expression for the value of the angle in the trigonometric function, let's do simplification, on solving we get:
\[\Rightarrow \cos (\theta )\cos (\theta ) = x \\
\Rightarrow {\cos ^2}(\theta ) = x \\
\Rightarrow \cos (\theta ) = \sqrt x \\
\therefore \theta = {\cos ^{ - 1}}\sqrt x \\ \]
Here, now we can get the value of the angle in the function, for a given value of the variable we can solve for the desired angle, which is our required solution for the question.

Note: Trigonometric function gives the value for a defined angle, this can be found by using the graph of the function also, for every trigonometric function we have a defined value, but for some angles the values are also undefined. We can search for both the angles as well as for the value for the given angle.