Question

The expression cos^-1 (3/5) has an infinite number of values.. True or False.

Answer 1

Answer:

True

Step-by-step explanation:

cos^-1 (3/5) has an infinite number of values means that there are infinite angles which cos^-1 is equal to 3/5.

Solving cos^-1 (3/5) = 53.13° = θ, but we know that cosine is a periodic function, i.e. its values are repeated at every 360°. So, if  cos 53.13 = 3/5 , then cos (53.13+n*360) = 3/5  is also satisfied, where n is an integer .

Answer 2

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:

$\arccos (\dfrac{3}{5})$

Let us equate this expression to be equal to some angle theta(θ)

i.e.

Let

$\arccos (\dfrac{3}{5})=\theta\\\\\cos \theta=\dfrac{3}{5}$

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:

$\cos \theta=\dfrac{3}{5}$

i.e. the expression:

$\arccos (\dfrac{3}{5})$ has infinite number of values.