Answer:
Step-by-step explanation:
Plot that point in the x/y coordinate plane to see that it sits in the third quadrant. From the point, draw a line to the origin, constructing a right triangle. The side adjacent to the angle is -2, the side across from the angle is -5, so we need to find the length of the hypotenuse using Pythagorean's Theorem:
[tex]c^2=(-5)^2+(-2)^2[/tex] and
[tex]c^2=25+4[/tex] so
[tex]c=\sqrt{29}[/tex]
That means that
[tex]sin\theta=-\frac{5}{\sqrt{29} }=-\frac{5\sqrt{29} }{29}[/tex] and
[tex]csc\theta=-\frac{\sqrt{29} }{5}[/tex]
That means that
[tex]cos\theta=-\frac{2}{\sqrt{29} }=-\frac{2\sqrt{29} }{29}[/tex] and
[tex]sec\theta=-\frac{\sqrt{29} }{2}[/tex]
It also means that
[tex]tan\theta=\frac{5}{2}[/tex] and
[tex]cot\theta=\frac{2}{5}[/tex]
