What fraction is between 4/8 and 1
2 answers:
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Answer: Choice A. sin(A) = cos(B)
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Explanation:
The rule is that sin(A) = cos(B) if and only if A+B = 90.
Note how
- sin(A) = opposite/hypotenuse = BC/AB
- cos(B) = adjacent/hypotenuse = BC/AB
Since both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).
In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.
The side lengths can be anything you want, as long as you're dealing with a right triangle.
Answer:
In this problem, we are given the following functions:
and its inverse function:
First of all, we want to calculate . This can be obtained by substituting
x = 2
into f(x). Doing so, we find:
Then we want to calculate . We can do it by substituting
x = 1
into . Doing so,
Then we want to calculate , which can be found by calculating f(2) and then using it as input for
We know that
f(2) = 1
Therefore,
Then we want to calculate , which can be calculated by plugging
x = -2
into . Doing so,
Then we want to calculate ; by substituting
x = 4
into f(x), we find
Finally, we want to find
We know already that
So we have: