# Equivalent expressions for values of cot and sec.

• Nov 14th 2009, 02:29 PM
TheCB4
Equivalent expressions for values of cot and sec.
Hello everyone, I do not understand what the question is asking nor do i understand how to do this, perhaps someone could help me?

1. Determine an equivalent expression in terms of the related actue angle

a) cot(-π/4) --answer is cot 3π /4

b) sec7π /6 --answer is sec5π /6

Thanks!
• Nov 14th 2009, 10:36 PM
Hello TheCB4
Quote:

Originally Posted by TheCB4
Hello everyone, I do not understand what the question is asking nor do i understand how to do this, perhaps someone could help me?

1. Determine an equivalent expression in terms of the related actue angle

a) cot(-π/4) --answer is cot 3π /4

b) sec7π /6 --answer is sec5π /6

Thanks!

An acute angle is one that is between $\displaystyle 0$ and $\displaystyle \pi/2$, so both of these answers are incorrect, as the angles are greater than $\displaystyle \pi/2$.

The first one should be $\displaystyle -\cot(\pi/4)$ and the second is $\displaystyle -\sec(\pi/6)$.

I think you should study the graphs of $\displaystyle y = \cot x$ and $\displaystyle y =\tan x$. For example, just here.

From these, you can work out (among other things) that
$\displaystyle \cot(-x) =-\cot (x)$ (which I used to answer question 1)
and
$\displaystyle \sec(\pi+x)=-\sec(x)$ (which I used to answer question 2)