Question

the formula for secant is:

1/x

the forumula for cosecant is:

1/y

for the coordinates (negative square root of 2/2, square root of 2/2) how come the cosecant is square root of 2 and the secant is negative square root of 2?

for my cosecant I got negative square root of 2/2 and for secant I got 2/negative square root of 2?

Answer 1

That is true if you are talking about a right triangle whose hypotenuse is 1, side opposite angle A is y and side adjacent to angle A is x.

You seem to be dealing with a point on a unit circle. With a negaive x value and a positive y value, it is in the second quadrant, and angle A 135 degrees.

Secants and cosecants always have values for which the absolute value is greater than or equal to 1.

In your case, x = -1/(sqrt 2) and y = 1/(sqrt2), so sec x = -sqrt 2 and csc x = sqrt 2
Note that (sqrt2)/2 = 1/sqrt2
That may be what is confusing you.