Question

What is the maximum value of $3 - 7\cos 5x$?

Answer 1

Hint: Before attempting this question, one should have prior knowledge about the concept of trigonometric fraction and also remember that the range of cos functions is [–1, 1] and to get maximum value, value of cos function should be – 1, using this information will help you to approach the solution of the question.

Complete step by step answer:
According to the given information we have equation $3 - 7\cos 5x$ taking this as equation 1
Let Y be the maximum value of the given function
As we know that for the cos function the range is [–1, 1]
So, the maximum value of cos function is equal to 1
But in the given equation to obtain the required maximum value the value of cos function must be equal to – 1
Therefore, to obtain the maximum value of the given equation cos5x = – 1
Now substituting the value of cos5x in the equation 1 we get
Y = 3 – 7 (- 1)
$ \Rightarrow $ Y = 3 + 7
$ \Rightarrow $ Y = 10

Therefore, the maximum value of the $3 - 7\cos 5x$ is equal to 10.

Note: In the above solution we came across the term “function” which can be explained as a relation between the provided inputs and the outputs of the given inputs such that each input is directly related to the one output. The representation of a function is given by supposing if there is a function f that belongs from X to Y then the function is represented by $f:X \to Y$examples of function are trigonometric function, binary function, etc.