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Answer:

To find the values of the six trigonometric functions for the angle θ with the terminal side passing through (5, –2), first identify the coordinates x = 5 and y = –2. Since the x-coordinate is positive and the y-coordinate is negative, the point is in Quadrant IV. Next, calculate the radius (r) using the Pythagorean theorem: r = √(5² + (–2)²) = √(25 + 4) = √29. Then apply the trigonometric definitions: sin(θ) = y/r = –2/√29 = –2√29/29 cos(θ) = x/r = 5/√29 = 5√29/29 tan(θ) = y/x = –2/5 csc(θ) = r/y = –√29/2 sec(θ) = r/x = √29/5 cot(θ) = x/y = –5/2