Find an equation using the cosecant function that has the sa

Find an equation using the cosecant function that has the same graph as y = sec x.

Question 9 options:

show your work

Solution

Lets take y = cosx and try and understand this....

We know that sin and cos are related by complementary angles...

And since the second quadrant has sine positive, we can state that
sin(pi/2 + x) = cosx
OR
sin(x + pi/2) = cosx

Inverting both sides :

1 / sin(x + pi/2) = 1 / cos(x)

csc(x + pi/2) = sec(x)

So, option A is the answer