trig radians

[ang0915]

Given the function f(x)=-2sin(4x)+1, determine all the values of x in the domain 0≤π≤2π when f(x)=3

 

[Otis]

Hi Ang. I would start by substituting the given value for f(x), followed by rearranging the equation to get the form

sin(4x) = Real number​

After that, I would determine the period of sin(4x).

Can you try those two things and show us what you get? If you need more help, we can continue from there.

 

[ang0915]

 

[Dr.Peterson]

Now, what does 4x have to equal? That is, for what values of u is sin(u) = -1?

 

[ang0915]

I ended up graphing it and wrote down the values of x when y=3, the maximum

 

[Otis]

I ended up graphing it

Ah, I didn't know that you were allowed to use a graph. That's always an easy choice, but I'd thought the exercise was assigned to practice developing a formula like:

[imath]x = \frac{3\pi}{8} + k\cdot\frac{\pi}{2}[/imath]

where k is an Integer. That gives all solutions, so we'd finish by evaluating it to find x-values within the required interval.