In Q4, the terminal ray of our reference angle is the hypotenuse of the right triangle created by connecting the end of the terminal ray to the positive x-axis. Theta is the angle between these 2. In the equation, in the simplest form, if we sub in a 1 for x, then y = -2. That means the distance along the x axis (the base of the right triangle) is 1, and the height of the triangle is -2. We need now to find the measure of the hypotenuse using Pythagorean's Theorem. [tex]c^2=1^2+(-2)^2[/tex] and [tex]c^2=5[/tex] so [tex]c= \sqrt{5} [/tex]. The sin of theta is the ratio of the side opposite over the hypotenuse, so [tex]sin \theta =- \frac{2}{ \sqrt{5} } [/tex], and [tex]csc \theta =- \frac{ \sqrt{5} }{2} [/tex]. [tex]cos \theta= \frac{1}{ \sqrt{5} } [/tex] and [tex]sec \theta = \frac{ \sqrt{5} }{1} [/tex]. [tex]tan \theta = -\frac{2}{1} [/tex] so [tex]cot \theta =- \frac{1}{2} [/tex]. There you go!
