use an inverse trig function to write è as a function of x
(There is a right triangle.
The hypotenuse is 2.
è is the angle between the base and the hypotenuse.
The base/adjacent side of è is (x + 1)
The side opposite è does not have a value.)
a) è = sqrt [4 - (x + 1)^2] all divided by 2
b)è = cos ^ -1 [(x + 1)/2]
c)è = tan ^ -1 [(x + 1)/2]
d)è = sin ^ -1 [2/(x + 1)]
How do I do this? I'm leaning towards B, the inverse cosine because only the adjacent side and hypotenuse are given. The opposite side is not given, and there is already a variable x in the given adjacent side.
You are correct in leaning towards using the inverse cosine function (option b).
In a right triangle, the cosine function is defined as the ratio of the adjacent side to the hypotenuse.
So, based on the given information, we have:
cos(è) = adjacent/hypotenuse
Since the length of the adjacent side is (x + 1), and the length of the hypotenuse is 2, we can write the equation as:
cos(è) = (x + 1)/2
And to solve for è, we can take the inverse cosine on both sides:
è = cos^(-1)((x + 1)/2)
Therefore, option B (è = cos^(-1)((x + 1)/2)) is the correct answer.
To find è as a function of x, we can use the inverse trigonometric function to relate the given sides of the right triangle.
In this case, the adjacent side is (x + 1) and the hypotenuse is 2. Since we are interested in the angle è, we need to use the inverse cosine function.
The correct answer is b) è = cos ^ -1 [(x + 1)/2].
The reason why the inverse cosine function is appropriate here is because it relates the adjacent side and the hypotenuse. Since the opposite side is not given, we cannot use the inverse sine or inverse tangent functions.
By substituting the values into the formula, we have:
è = cos ^ -1 [(x + 1)/2].
This equation gives us the angle è as a function of x, where x is the length of the adjacent side.
Thus, the correct answer is b) è = cos ^ -1 [(x + 1)/2].