# Equivalent Trig Expressions

#### Pumpkin99

Given that cot (13pi/14)= tan z, find angle z.
So I used cot x=tan(pi/2-x), and I got the answer -3pi/7, but the answer says it's positive, so I am confused.

#### greg1313

Forum Staff
$$\displaystyle \tan\left(x + \frac{\pi}{2}\right) = -\cot(x)$$

$$\displaystyle \frac{13\pi}{14} + \frac{\pi}{2} = \frac{10\pi}{7}$$

$$\displaystyle -\tan(x) = \tan(-x) \Rightarrow \tan\left(-\frac{10\pi}{7}\right) = \tan\left(-\frac{3\pi}{7}\right),\,z = - \frac{3\pi}{7}$$

Last edited by a moderator:

#### niki500

Yes, it is correct and tg must be negative because cotangent is in II. Quadrant. Maybe in your book there is positive solution because if you add 2pi to -3pi/7 you get the same angle 2pi+(-3pi/7)=11pi/7 but in positive direction.

Last edited by a moderator:

thank you!

#### greg1313

Forum Staff
More accurately, $$\displaystyle z = -\frac{3\pi}{7} + k\pi,\,k \in \mathbb{Z}$$

Last edited by a moderator:

#### skipjack

Forum Staff
I suspect that the book's answer was $4\pi$/7.