Question

sec theta = 5/3 then what is the value of theta?..... help me guys.. ​

Answer 1

This is a complex question.

There can be four solutions but not accurate.

First one can be;

$\large\rm { \theta = 2 \pi n_{1} + \arctan \bigg ( \frac{4}{3} \bigg ) }$

where

$\large\rm { n_{1} \in Z}$

Second one can be;

$\large\rm { \theta = 2 \pi n_{2} + 2 \pi - \arctan \bigg ( \frac{4}{3} \bigg ) }$

where

$\large\rm { n_{2} \in Z}$

Third one can be;

$\large\rm { \theta = 2 \pi n_{1} + \arccos \bigg ( \frac{3}{5} \bigg ) }$

Fourth one can be;

$\large\rm { \theta = 2 \pi n_{2} + 2 \pi - \arccos \bigg ( \frac{3}{5} \bigg ) }$

In both (3),(4) , $\large\rm { n_{1} \ and \ n_{2} \in Z}$