Answer:
Step-by-step explanation: To find the exact values of the trigonometric functions for the point K(-2, 4) on the terminal side of an angle θ, we can use the coordinates of the point to determine the ratios.
First, let's calculate the values:
Cosine (cos) θ:
Cos θ = adjacent/hypotenuse
Since the x-coordinate of the point is -2 and the distance from the origin (hypotenuse) is √((-2)^2 + 4^2) = √4 + 16 = √20 = 2√5,
we have:
Cos θ = -2 / (2√5) = -√5/√5 = -1
Secant (sec) θ:
Sec θ = 1 / Cos θ
Since we found that Cos θ = -1, we have:
Sec θ = 1 / (-1) = -1
Tangent (tan) θ:
Tan θ = opposite/adjacent
Since the y-coordinate of the point is 4 and the x-coordinate is -2, we have:
Tan θ = 4 / (-2) = -2
Cotangent (cot) θ:
Cot θ = 1 / Tan θ
Since we found that Tan θ = -2, we have:
Cot θ = 1 / (-2) = -1/2
The exact values of the trigonometric functions for the given point are:
Cos θ = -1
Sec θ = -1
Tan θ = -2
Cot θ = -1/2