Trigonometry: At which quadrant should the angle lie?

[LiHJ]

Homework Statement

Dear Mentors,

I have some doubts on this question that I was doing from my textbook.
Question:
Given that tan A =(-2), find the exact value of sin(-A)

My doubts are:
For angle A to be negative, angle A should be on the 2nd or 4th quadrant. But than I will have 2 possible answers. However the textbook only give 1 answer.

So I further analyze again. If the question didn't specify on how angle A is like should we stick to the principle value. Since principle value of tan is from -90 degree to 90 degree. Than angle A should be at the 4th quadrant only. So sin(-A)= - sin(A), sin A = -(-2/√5)= 2/(√5) which is the answer as given.

Can any Mentors please advise me on this. Whether I'm thinking correctly.

Thank you so much.

Homework Equations

The Attempt at a Solution

 

[eumyang]

Homework Statement

Dear Mentors,

I have some doubts on this question that I was doing from my textbook.
Question:
Given that tan A =(-2), find the exact value of sin(-A)

My doubts are:
For angle A to be negative, angle A should be on the 2nd or 4th quadrant. But than I will have 2 possible answers. However the textbook only give 1 answer.

Some math books will indicate a restricted domain by capitalizing the trig functions, ie. Tan x (which would have a domain of -π/2 < x < π/2). (So, in your book, was the "T" capitalized?) I wasn't familiar with this notation, but regardless, when I see a (regular) trig function I do not assume that one should stick with the principal values. So if I were to do this problem I would have two answers. Maybe it's a typo in the answer section, or maybe there's more to the problem than what's given here.

 

[LiHJ]

Thanks for the reply
But in this book they do not use such notation such as Tan or tan to distinguish between the two. They only use tan.

I actually written to the publisher about this question. But I didn't have any reply.