CotA =5/12then sinA+cosa=?

May 12, 2018

$\sin A + \cos A = \frac{17}{13}$

Explanation:

$\cot A = \frac{5}{12}$
thus the hypotenuse is:
$h = \sqrt{25 + 144} = 13$
$\sin A = \frac{12}{13}$
$\cos A = \frac{5}{13}$
$\sin A + \cos A = \frac{12}{13} + \frac{5}{13} = \frac{17}{13}$

May 13, 2018

$\sin A + \cos A = \pm \frac{17}{13}$

Explanation:

Use trig identities to find sin A and cos A
${\cos}^{2} A = \frac{1}{1 + {\tan}^{2} A} = \frac{1}{1 + \frac{25}{144}} = \frac{144}{169}$
$\cos A = \pm \frac{12}{13}$
$\cot A = \frac{5}{12}$ --> A could be in Q. 1 or Q. 3.
${\sin}^{2} A = 1 - {\cos}^{2} A = 1 - \frac{144}{169} = \frac{25}{169}$
$\sin A = \pm \frac{5}{13}$
If A is in Quadrant 1 -->
$\sin A + \cos A = \frac{12}{13} + \frac{5}{13} = \frac{17}{13}$
If A is in Quadrant 3 -->
$\sin A + \cos A = - \frac{12}{13} - \frac{5}{13} = - \frac{17}{13}$
Answer: $\sin A + \cos A = \pm \frac{17}{13}$