Why Are My Trig Ratios csc and sec Incorrect for (7π)/4?

[Veronica_Oles]

Homework Statement

The question states to find the primary trig ratios for (7π)/4

Homework Equations

The Attempt at a Solution

I got
sin= (-√2)/2
cos=(√2)/2
tan= -1
csc= 2/(-√2)
sec= 2/(√2)
cot= -1

I got all of them correct except for csc and sec, and I am unsure why the solutions are telling me
csc = -√2
sec = √2
I thought my original answers were correct because csc is reciprocal of sin and sec is reciprocal of cos.
Can someone help me make sense of this?

 

[fresh_42]

Write $2= \sqrt{2}\,\cdot\,\sqrt{2}$ and cancel one root factor.

 

[SammyS]

Homework Statement

The question states to find the primary trig ratios for (7π)/4

Homework Equations

The Attempt at a Solution

I got
sin= (-√2)/2
cos=(√2)/2
tan= -1
csc= 2/(-√2)
sec= 2/(√2)
cot= -1

I got all of them correct except for csc and sec, and I am unsure why the solutions are telling me
csc = -√2
sec = √2
I thought my original answers were correct because csc is reciprocal of sin and sec is reciprocal of cos.
Can someone help me make sense of this?

Rationalize the denominators.