1. ## Related Acute Angle

Hi,

I hope someone can help. I'm trying to understand why the equivalent expression in terms of the related acute angle for sec(7pi/6) is -sec(pi/6). I understand why the answer is sec(pi/6), but I don't see why there is a negative sign in-front of the solution. Can someone please explain why?

I'd really appreciate help

Sincerely,
Olivia

3. ## Re: Related Acute Angle

Originally Posted by otownsend
I hope someone can help. I'm trying to understand why the equivalent expression in terms of the related acute angle for sec(7pi/6) is -sec(pi/6). I understand why the answer is sec(pi/6), but I don't see why there is a negative sign in-front of the solution. Can someone please explain why?
1. Do you understand that $\cos\left(\theta\right)=\cos\left(\theta-2\pi\right)$ You said you did$~??\\$
2. Do you understand that $\cos\left(\theta\right)$ is an odd function, $\cos\left(-\theta\right)=-\cos\left(\theta\right)\\$
3. Do you understand that $\sec\left(\theta\right)$ is $\frac{1}{\cos\left(\theta\right)}\\$
4. Does it follow that on its domain $\sec(x)$ is an odd function? $\sec(-x)=-\sec(x)$

4. ## Re: Related Acute Angle

I understand #1.

I don't understand #2. I thought that cosine is an even function and sine is an odd function. Is this different?

I understand #3.

In order to understand #4, I probably need an explanation on #2.

5. ## Re: Related Acute Angle

Originally Posted by otownsend
I understand #1.

I don't understand #2. I thought that cosine is an even function and sine is an odd function. Is this different?

I understand #3.

In order to understand #4, I probably need an explanation on #2.
You are correct. I just mixed the two up. sorry about that.

$\frac{{7\pi }}{6} - 2\pi = - \frac{{5\pi }}{6} \in III$

Cosine & hence secant are negative in III. The reference angle is $\frac{{1\pi }}{6}$

But being in III makes the answer $-\sec\left(\frac{{1\pi }}{6}\right)$

6. ## Re: Related Acute Angle

Makes sense. Thanks!