If θ is an angle in standard position and its terminal side passes through the point (5,7), find the exact value of cscθ in simplest radical form.
Construct a right-angled triangle in quad I with the line joining
(5,7) to the origin as its hypotenuse
so we have x^2 + y^2 = r^2
5^2 + 7^2 = r^2
r = √74
Using the standard definitions of the 6 trig functions, we can now
state any one of them.
cscθ = 1/sinθ , and since sinθ = 7/√74
cscθ = √74 / 7