In class today we went over how to properly solve an equation that has inverse cosine in it after being simplified. So far we have only been asked to find the given function value (solve f(x) when x= 7.8) and find the first three positive values of x for the given values of f(x).

Example:

Solve the equation above for f(7.8)

To do this all you need to do is plug 7.8 into the equation for x. Once you do that all you need to do is type it into your calculator with the appropriate parentheses. You should get 2.314.

B. Find the first three positive values of x when f(x) = 6.

First, plug in six for f(x):

Then subtract two from both sides.

Then divide by 5.

In order to get rid of the cosine, you must

take the inverse cosine on the other side

of the equation.

After that you just multiply by pi over 10

and add 3.

In order to find the first three positive answers you must plug the inverse cosine of 4 over 5 into 2 equations:

1. The calculator answer of the inverse cosine of 4 over 5 + 2 times pi times n

2. 2 times pi - the calculator answer

After that all thats left to do is simplify and plug in numbers for n to see what will give us the smallest positive answers.

The first equation gives you:

The second equation gives you:

Then you distribute the 10 over pi and simplify

The first equation gives you:

The Second equation gives you:

Then you substitute numbers in for n (normally between -1 and 1) and those will get you the first three positive numbers of the graph when f(x) = 6

When you plug in 0 for n, the first equation gives you 5.0483 and the second equation gives you 20.9517

When you plug in -1 for n, it doesn't work for the first equation because it gives you a negative number. But, when you plug it into the second equation you get .9517

Therefore, the answers to the second part of this question are: .9517, 5.0483, 20.9517