Let (-2,-3) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.

Answer 1

Make a sketch with a point at x = -2, y = -3, thereby lying in quadrant III. Draw a line from the negative x-axis down to this point, constructing a right triangle. The hypotenuse is then √13. cos θ = -2 /√13 = -2 √13 /13.

csc θ = 1/sin θ = - √13 /3. tan θ = (-3) /(-2) = 3/2.