Given the triangle shown, describe the function values in term of the triangle's two legs
/|
/a| y
/ |
/o__|
x
Find: sec a
Find: csc o
secant= hypotenuse/adjacent side
cosecant=hypotenuse/opposite side
I know its hard to see, but the triangle looks like this /_| with the legs on the right and bottom with the hypotenuse on the left. They give you y for the right leg and x for the bottom leg, no hypotneuse. o is the bottom right angle and a is the top right angle. So I don't know how to get hypotenuse.
The side opposite the right angle is the hypotenuse. Memorize that.
To find the function values sec a and csc o, we first need to understand what these functions represent.
In a right triangle, sec a (secant of angle a) is the ratio of the length of the hypotenuse to the length of the side adjacent to angle a.
csc o (cosecant of angle o) is the ratio of the length of the hypotenuse to the length of the side opposite to angle o.
Now, let's use the given triangle to find the function values.
Given that angle a is adjacent to side x and angle o is opposite to side y:
To find sec a:
1. We need to find the length of the hypotenuse. We can use the Pythagorean theorem, which states that the square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides (a^2 + b^2).
2. In this case, the length of the hypotenuse (c) is equal to √(x^2 + y^2).
3. Now, the sec a value is equal to the length of the hypotenuse (c) divided by the length of the side adjacent to angle a (x).
So, sec a = c / x = (√(x^2 + y^2)) / x.
To find csc o:
1. Again, we need to find the length of the hypotenuse, which is √(x^2 + y^2).
2. The csc o value is equal to the length of the hypotenuse (c) divided by the length of the side opposite angle o (y).
So, csc o = c / y = (√(x^2 + y^2)) / y.
Therefore, the function values are:
sec a = (√(x^2 + y^2)) / x
csc o = (√(x^2 + y^2)) / y.
Note: The given triangle information is essential to determine the function values.