csat-suneung 2022 Q7

csat-suneung · South-Korea · csat__math 3 marks Reciprocal Trig & Identities

For $\theta$ satisfying $\pi < \theta < \frac { 3 } { 2 } \pi$ and $\tan \theta - \frac { 6 } { \tan \theta } = 1$, what is the value of $\sin \theta + \cos \theta$? [3 points]
(1) $- \frac { 2 \sqrt { 10 } } { 5 }$
(2) $- \frac { \sqrt { 10 } } { 5 }$
(3) 0
(4) $\frac { \sqrt { 10 } } { 5 }$
(5) $\frac { 2 \sqrt { 10 } } { 5 }$

For $\theta$ satisfying $\pi < \theta < \frac { 3 } { 2 } \pi$ and $\tan \theta - \frac { 6 } { \tan \theta } = 1$, what is the value of $\sin \theta + \cos \theta$? [3 points]\\
(1) $- \frac { 2 \sqrt { 10 } } { 5 }$\\
(2) $- \frac { \sqrt { 10 } } { 5 }$\\
(3) 0\\
(4) $\frac { \sqrt { 10 } } { 5 }$\\
(5) $\frac { 2 \sqrt { 10 } } { 5 }$

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