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Please need answer 17.

Please need answer 17.-example-1

1 Answer

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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

Please need answer 17.-example-1
User JP Duffy
by
7.8k points

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