Did I get these trig questions right? (If P(1,-5) is on terminal arm of theta, find sec(theta).)

[breadsticks]

 

[The Highlander]

View attachment 35391

Yes but there is a mistake in your evaluation of "c" and this label has suddenly appeared out of nowhere! It should have been marked on your sketch so the reader knows what you are trying to calculate as shown on your amended sketch (extract), below.

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[Steven G]

My biggest concern is that you never stated what sec(theta) equals. That is, somewhere on the page it should say sec(theta) = sqrt(26)

 

[Steven G]

Yes but there is a mistake in your evaluation of "c" and this label has suddenly appeared out of nowhere! It should have been marked on your sketch so the reader knows what you are trying to calculate as shown on your amended sketch (extract), below.

View attachment 35393​

1^2 + ^-5^2 = 1+(-25) = 1-25=-24
To OP: It really should be 1 + (-5)^2 but that does equal 1 + 5^2 so you are OK. The Highlander is correct about there being a + sign where you have a - sign.