-2x+15y =-327x - 5y=17
1 answer:
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Answer:
The given function symmetric about the y-axis.
Step-by-step explanation:
The given function is
.... (1)
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r,-θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
Put (r, -θ ) in the given function.
Therefore it is not symmetric about x-axis.
Put (-r, -θ ) in the given function.
Therefore it is symmetric about y-axis.
Put (-r,θ ) in the given function.
Therefore it is not symmetric about the origin.
In order to answer this question, the figure in the first picture will be helpful to understand what a right triangle is. Here, a right angle refers to .
However, if we want to solve the problem we have to know certain things before:
In the second figure is shown a general right triangle with its three sides and another given angle, we will name it :
- The side <u>opposite to the right angle</u> is called The Hypotenuse (h)
- The side <u>opposite to the angle
</u> is called the Opposite (O)
- The side <u>next to the angle
So, going back to the triangle of our question (first figure):
- The Hypotenuse is AB
- The Opposite is BC
- The Adjacent is AC
Now, if we want to find the length of each side of a right triangle, we have to use the <u>Pythagorean Theorem</u> and T<u>rigonometric Functions:</u>
Pythagorean Theorem
(1)
Trigonometric Functions (here are shown three of them):
Sine: (2)
Cosine: (3)
Tangent: (4)
In this case the function that works for this problem is cosine (3), let’s apply it here:
(5)
And we will use the Pythagorean Theorem to find the hypotenuse, as well:
(6)
(7)
Substitute (7) in (5):
Then clear BC, which is the side we want:
Finally is approximately 13 cm
