Find the indicated trigonometric function, given that è is an angle in standard position with the terminal side passing
through the given point.
2) (15, 20); Find csc è.
A) 5/3
B) 3/4
C) 5/4
D) 4/3
tanA = 20/15 = 4/3 = Y/X.
r^2 = X^2 + Y^2,
r^2 = 3^2 + 4^2 = 25,
r = 5.
sinA = Y/r = 4/5,
cscA = 1/sinA = 5/4.
To find the cosecant (csc) of an angle, we need to find the reciprocal of the sine function.
In this problem, we are given a point (15, 20), which represents an x-coordinate of 15 and a y-coordinate of 20. To find the angle è in standard position with the terminal side passing through this point, we can use the properties of right triangles.
We can create a right triangle by drawing a line from the origin to the given point (15, 20). The length of the horizontal leg of the triangle is 15, and the length of the vertical leg is 20.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse^2 = horizontal leg^2 + vertical leg^2
hypotenuse^2 = 15^2 + 20^2
hypotenuse^2 = 225 + 400
hypotenuse^2 = 625
Taking the square root of both sides, we find that the hypotenuse is 25.
Now, we can use the properties of the right triangle to find the sine of the angle è. The sine of an angle is equal to the length of the vertical leg divided by the length of the hypotenuse.
So, sine(è) = vertical leg / hypotenuse
sine(è) = 20 / 25
sine(è) = 4 / 5
Finally, to find the cosecant of the angle è, we take the reciprocal of the sine:
cosecant(è) = 1 / sine(è)
cosecant(è) = 1 / (4 / 5)
cosecant(è) = 5 / 4
Therefore, the cosecant of the angle è is 5/4, which is option C in the multiple-choice answers.