Find the values of the six trigonometric functions of the angle in standard position with the terminal side passing through the point P(-4, 3).

To find the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) of an angle, we can use the given point P(-4, 3) to determine the lengths of the sides of the triangle formed.

Let's first find the length of the hypotenuse, which can be calculated using the distance formula:

Distance = √((-4 - 0)^2 + (3 - 0)^2)
= √((-4)^2 + (3)^2)
= √(16 + 9)
= √25
= 5

Now, we have the length of the hypotenuse (5) and the coordinates of point P(-4, 3). To find the values of the trigonometric functions, we need to divide the lengths of the sides of the triangle formed by P(-4, 3) by the hypotenuse (5).

Let's label the sides of the triangle as follows:
- Opposite: the side opposite to the angle (in this case, side y, which corresponds to the y-coordinate of P)
- Adjacent: the side adjacent to the angle (in this case, side x, which corresponds to the x-coordinate of P)

Using the coordinates of P(-4, 3), we can determine the lengths of the sides:
- Opposite (y) = 3
- Adjacent (x) = -4

Now, we can calculate the values of the trigonometric functions as follows:

Sine (sin): sinθ = Opposite / Hypotenuse
sinθ = 3 / 5

Cosine (cos): cosθ = Adjacent / Hypotenuse
cosθ = -4 / 5

Tangent (tan): tanθ = Opposite / Adjacent
tanθ = 3 / -4

Cosecant (csc): cscθ = 1 / sinθ

Secant (sec): secθ = 1 / cosθ

Cotangent (cot): cotθ = 1 / tanθ

Therefore, the values of the six trigonometric functions for the angle in standard position with the terminal side passing through the point P(-4, 3) are:
sinθ = 3/5
cosθ = -4/5
tanθ = -3/4
cscθ = 5/3
secθ = -5/4
cotθ = -4/3

draw the triangle.

then, write the functions.

TanTheta=-3/4

You finish it.