Question

For a standard position angle determined by the point (5,12), what are the values of the trigonometric functions? Find cscθ and secθ

Answer 1

First, we need to determine which quadrant the point (5,12) falls in. Since both the x and y coordinates are positive, the point is in the first quadrant.

Next, we can use the Pythagorean theorem to find the hypotenuse:
r = √(5^2 + 12^2) = √(25 + 144) = √169 = 13

Now, we can determine the values of the trigonometric functions:
sinθ = y/r = 12/13 = 12/13
cosθ = x/r = 5/13 = 5/13
tanθ = y/x = 12/5 = 12/5
cscθ = 1/sinθ = 1/(12/13) = 13/12
secθ = 1/cosθ = 1/(5/13) = 13/5