Given the coordinates of the terminal side of an angle in standard position,

find the value of sine, cosine, and tangent:

(-4,0)

To find the values of sine, cosine, and tangent of an angle with the terminal side at (-4,0) in standard position, we need to calculate the ratio of the y-coordinate to the hypotenuse, the ratio of the x-coordinate to the hypotenuse, and the ratio of the y-coordinate to the x-coordinate, respectively.

Let's denote the angle as θ.

First, we need to find the hypotenuse. The hypotenuse is the distance from the origin to the point (-4,0), which can be calculated using the distance formula:

hypotenuse = √((-4 - 0)^2 + (0 - 0)^2)
= √((-4)^2 + 0)
= √(16)
= 4

Now, we can calculate the values of sine, cosine, and tangent:

sine(θ) = y-coordinate / hypotenuse
= 0 / 4
= 0

cosine(θ) = x-coordinate / hypotenuse
= -4 / 4
= -1

tangent(θ) = y-coordinate / x-coordinate
= 0 / -4
= 0

Therefore, for the angle with the terminal side at (-4,0) in standard position, the value of sine is 0, the value of cosine is -1, and the value of tangent is 0.

To find the values of sine, cosine, and tangent for an angle in standard position, we need to use the given coordinates of the terminal side.

Given the coordinates (-4, 0), we can determine the length of the hypotenuse and the values of sine, cosine, and tangent.

First, let's label the sides of the right triangle formed by the angle:

|
|
(-4,0) |
|______________________

Based on this right triangle, the adjacent side (adj) represents the x-coordinate (-4), the opposite side (opp) is the y-coordinate (0), and the hypotenuse (hyp) is the distance from the origin to the point (-4,0).

Using the Pythagorean theorem, we can find the length of the hypotenuse (hyp):

hyp = √(adj^2 + opp^2)
= √((-4)^2 + 0^2)
= √(16 + 0)
= √16
= 4

Now, we can find the values of sine, cosine, and tangent:

Sine (sin):
sin = opp/hyp
= 0/4
= 0

Cosine (cos):
cos = adj/hyp
= -4/4
= -1

Tangent (tan):
tan = opp/adj
= 0/(-4)
= 0

Therefore, for the given coordinates (-4, 0), the values of sine, cosine, and tangent are:
sin = 0
cos = -1
tan = 0