Answer:
- sec(θ) = √10/3
- tan(θ) = 1/3
Explanation:
You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.
Trig functions
The relations between the angle and its trig functions are ...
Tan = Opposite/Adjacent
Sec = Hypotenuse/Adjacent
Unit circle
We have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...
tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line
sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3
The tangent is 1/3; the secant is (√10)/3.
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Additional comment
A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.
Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV