given csc θ= 5/4, determine tan θ if pi/2 < θ < pi
2 years ago
I'll be using the coordinates x, y, and r as though we're looking at a unit circle for this solution.
csc is a ratio of r/y
tan is a ratio of y/x
We know r = 5, y = 4, so x must be +/- 3 (this is a 3/4/5 triangle)
To figure out whether it's +/-, we have to consider what quadrant we're on (pi/2 to pi) this would be the negative x-axis
So now we know x = -3
This means tan = -4/3
2 years ago
Answered By Emily D
I'll be using the coordinates x, y, and r as though we're looking at a unit circle for this solution.
csc is a ratio of r/y
tan is a ratio of y/x
We know r = 5, y = 4, so x must be +/- 3 (this is a 3/4/5 triangle)
To figure out whether it's +/-, we have to consider what quadrant we're on (pi/2 to pi) this would be the negative x-axis
So now we know x = -3
This means tan = -4/3