Question

sec(pi + theta) is negative right?
@ganeshie8

Answer 1

we got a doubt, so lets derive it and see... :)

Answer 2

\[\sec (\pi + \theta) = \dfrac{1}{\cos(\pi + \theta)}\]

Answer 3

okay! :)

Answer 4

yes

Answer 5

use angle sum identity for the denominator

Answer 6

\[\sec (\pi + \theta) = \dfrac{1}{\cos(\pi + \theta)} = \dfrac{1}{\cos \pi \cos \theta - \sin \pi \sin \theta}\]

Answer 7

yess

Answer 8

whats the value of \(\sin \pi\) ?

Answer 9

whats the value of \(\cos \pi\) ?

Answer 10

Negative as it lies in third quadrant

Answer 11

sin 180 = 0
cos 180 = -1

Answer 12

yes i think it would be negative as it lies in third quadrant where sec is negative

Answer 13

\[\sec (\pi + \theta) = \dfrac{1}{\cos(\pi + \theta)} = \dfrac{1}{\cos \pi \cos \theta - \sin \pi \sin \theta} = \dfrac{1}{-1 \cos \theta - 0\sin \theta} \]

Answer 14

Yes @No.name

Answer 15

\[= \dfrac{1}{ \cos \theta } = -\sec \theta \]

Answer 16

thats a good observation ! if all we want to know is the polarity

Answer 17

thanks , well i found a way in my book to remember it , i will post it for others to see

Answer 18

these are always tricky, would love to see it :)