Find cos ( 2 ⋅ ∠ A B C ) cos(2⋅∠ABC)
1 answer:
The value of the cosine function is -0.385
<h3>How to determine the measure of the cosine function?</h3>The figure that completes the question is added as an attachment
From the figure, we have the following sides
AB = √13
AC = 3
BC = 2
The triangle is a right triangle.
The angle B is calculated as:
cos(B) = 2/√13
Evaluate
cos(B) = 0.5547
Take the arccos of both sides
B = 56.31
This means that:
cos(ABC) = cos(56.31)
Multiply ABC by 2.
So, we have:
cos(ABC * 2) = cos(56.31 * 2)
Evaluate the product
cos(ABC * 2) = cos(112.62)
Evaluate the cosine
cos(ABC * 2) = -0.385
Hence, the value of the cosine function is -0.385
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Summary of even and odd functions
A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.
A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f.
From the definition itself, we see how can we test if the functions are even or odd.
- First graph (to the left)
From the graph, we see that the function is symmetric with respect to the y-axis because the left side (x<0) is a reflection (along the y-axis) of the right side (x>0), so it is an even function.
- Second graph (to the right)
From the graph, we see that the function is symmetric with respect to the origin, the left side (x<0) is a reflection (along with the origin) of the side to the right (x>0), so it is an odd function.
- First function (to the left)
The function:
is an even function because we see that:
- Second function (to the right)
The function:
is an odd function because we see that:
Summary
We have the following results:
- First function (to the left): even
- Second graph (to the right): odd
- First function (to the left): even
- Second function (to the right): odd