Evaluate (if possible) the function at the given values of the independent variable. Simplify the results. (If an answer is undefined, enter UNDEFINED.)
f(x)=sin x
f(pi)=
f(5pi/4)
f(fpi/30
f(pi) = 0
f(5pi/4) = -1/√2
dunno what the heck f(fpi/30 is, but
f(pi/3) = √3/2
To evaluate the function f(x) = sin(x) at the given values of the independent variable, we substitute the values into the function and simplify the results.
Let's start by evaluating f(pi):
f(pi) = sin(pi)
Since the sine function has a period of 2π, we know that sin(pi) is equal to sin(pi - 2π). Therefore, we have:
f(pi) = sin(pi) = sin(pi - 2π) = sin(-pi)
Using the symmetry property of the sine function, we can rewrite sin(-pi) as -sin(pi):
f(pi) = sin(-pi) = -sin(pi)
Next, let's evaluate f(5pi/4):
f(5pi/4) = sin(5pi/4)
The angle 5pi/4 is in the third quadrant, where sine is negative. Therefore, we can write sin(5pi/4) as -sin(pi/4):
f(5pi/4) = -sin(pi/4)
Finally, to evaluate f(fpi/30), we need to know the value of fpi/30. However, it seems like there is a typo in the expression. It should be f(pi/30) instead of f(fpi/30). Let's evaluate it:
f(pi/30) = sin(pi/30)
We can keep this expression as it is since there are no further simplifications. Therefore, the result is:
f(pi/30) = sin(pi/30)
In summary:
f(pi) = -sin(pi)
f(5pi/4) = -sin(pi/4)
f(pi/30) = sin(pi/30)