Question

The most general value of $\theta$ satisfying the equation

$\tan \theta = - 1$ and $\cos \theta = \frac { 1 } { \sqrt { 2 } }$is

• A. $n \pi + \frac { 7 \pi } { 4 }$
• B. $n \pi + ( - 1 ) ^ { n } \frac { 7 \pi } { 4 }$
• C. $2 n \pi + \frac { 7 \pi } { 4 }$
• D. None

Answer 1

Answer: (C)

$2 n \pi + \frac { 7 \pi } { 4 }$

Answer 2

$\tan \theta = - 1 = \tan \left( 2 \pi - \frac { \pi } { 4 } \right)$ and $\cos \theta = \frac { 1 } { \sqrt { 2 } } = \cos \left( 2 \pi - \frac { \pi } { 4 } \right)$

Hence, general value is $2 n \pi + \left( 2 \pi - \frac { \pi } { 4 } \right) = 2 n \pi + \frac { 7 \pi } { 4 }$