What is the value of sec theta given the diagram below?
Accepted Solution
A:
Answer:[tex]\sec \theta=-\sqrt{5}[/tex]Step-by-step explanation:The hypotenuse is [tex]h^2=6^2+3^2[/tex][tex]h^2=36+9[/tex][tex]h^2=45[/tex][tex]h=\sqrt{45}[/tex][tex]h=3\sqrt{5}[/tex]The terminal side of [tex]\theta[/tex] is in the second quadrant.In this quadrant; the secant ratio is negative.[tex]\sec \theta=-\frac{hypotenuse}{adjacent}[/tex][tex]\sec \theta=-\frac{3\sqrt{5}}{3}[/tex][tex]\sec \theta=-\sqrt{5}[/tex]