Answer:
The given statement:
The expression cos^-1 (3/5) has an infinite number of values is a true statement.
Step-by-step explanation:
We are given a expression as:
![\arccos (\dfrac{3}{5})](https://tex.z-dn.net/?f=%5Carccos%20%28%5Cdfrac%7B3%7D%7B5%7D%29)
Let us equate this expression to be equal to some angle theta(θ)
i.e.
Let
![\arccos (\dfrac{3}{5})=\theta\\\\\cos \theta=\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Carccos%20%28%5Cdfrac%7B3%7D%7B5%7D%29%3D%5Ctheta%5C%5C%5C%5C%5Ccos%20%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D)
As we know that the limit point of the cosine function is [-1,1]
i.e. it takes the value between -1 to 1 and including them infinite number of times.
Also,
-1< 3/5 <1
This means that the cosine function takes this value infinite number of times.
That is there exist a infinite number of theta(θ) for which:
![\cos \theta=\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D)
i.e. the expression:
has infinite number of values.