Question

The line with equation x−y=0 coincides with the terminal side of an angle θ in standard position in Quadrant III .

What is the value of tanθ

Answer 1

value of tanθ = 1

Explanation:

Given the line of the equation: x -y = 0

We can write this as;

y = x.

In Quadrant III, value of tangent is positive i.e,
`\tan \theta >0`

We know the equation of line is given by : y=mx+b where m is the slope of line and b is the y-intercept.

On comparing with the given equation:

m =1 , b = 0

Since, slope(m) = 1

Using Slope(m) =
`\tan \theta`

therefore, the value of tanθ = 1

Answer 2

The line x - y = 0 or x = y divides the 3rd quadrant into two equal parts.
Thus θ = 45
Therefore, Tan θ = tan 45 = 1