Question

If m is slope of a line and m=sec theta where theta us in deleted real neighborhood of π\2 then the possible angle between line any x axis is​

Answer 1

If m is the slope of a line and m=secθ where θ∈(0,π/2), then the possible angle between the line and the x-axis is​ π/2.

Given:

The slope of a line, m=secθ

To find:

The possible angle between the line and the x-axis

Solution:

The slope of a line represents the measure of the steepness and the direction of a line. If the angle of inclination of a line with the x-axis is θ, then the slope of the given line is given by tanθ.

∴ m=tanθ

⇒secθ=tanθ

This is only possible when θ=π/2.

Therefore, if m is the slope of a line and m=secθ where θ∈(0,π/2), then the possible angle between the line and the x-axis is​ π/2.

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