Answer:
sin θ = -2 / √(53)
sec θ = √(53) / 7
tan θ = -2 / 7
Explanation:
To find the exact values of sin θ, sec θ, and tan θ when the terminal side of angle θ passes through the point (7, -2), we can use the Pythagorean Theorem and the definitions of trigonometric functions.
Let's denote θ as the angle formed with the positive x-axis.
To find sin θ, we use the y-coordinate of the point (7, -2) divided by the radius (distance from the origin to the point):
sin θ = y / r = -2 / √(7² + (-2)²) = -2 / √(53)
To find sec θ, we use the x-coordinate of the point (7, -2) divided by the radius:
sec θ = r / x = √(7² + (-2)²) / 7 = √(53) / 7
To find tan θ, we use the y-coordinate of the point (7, -2) divided by the x-coordinate:
tan θ = y / x = -2 / 7
So, the exact values are:
sin θ = -2 / √(53)
sec θ = √(53) / 7
tan θ = -2 / 7