We can use the coordinates of point P (-5, 5) to find the values of the trigonometric functions for the angle formed between the positive x-axis and the line passing through the origin and point P.
First, we can find the distance from the origin to point P using the Pythagorean theorem:
r = sqrt((-5)^2 + 5^2) = sqrt(50)
Next, we can use the fact that the sine of an angle is equal to the y-coordinate of a point on the unit circle and the cosine of an angle is equal to the x-coordinate of a point on the unit circle. Since the radius of the unit circle is 1, we need to divide the x and y coordinates of point P by sqrt(50) to get the values for sine and cosine:
sin(θ) = y/r = 5/sqrt(50) = (5/10)sqrt(2) = (1/2)sqrt(2)
cos(θ) = x/r = -5/sqrt(50) = -(5/10)sqrt(2) = -(1/2)sqrt(2)
Next, we can use the fact that the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle:
tan(θ) = sin(θ)/cos(θ) = (1/2)sqrt(2)/(-(1/2)sqrt(2)) = -1
Similarly, we can use the reciprocal identities to find the values of the other three trigonometric functions:
csc(θ) = 1/sin(θ) = sqrt(2)
sec(θ) = 1/cos(θ) = -sqrt(2)
cot(θ) = 1/tan(θ) = -1
Therefore, the exact values of the six trigonometric functions for the angle formed by the line passing through the origin and point P (-5, 5) are:
sin(θ) = (1/2)sqrt(2)
cos(θ) = -(1/2)sqrt(2)
tan(θ) = -1
csc(θ) = sqrt(2)
sec(θ) = -sqrt(2)
cot(θ) = -1
IG:whis.sama_ent