# If 2sinA = 1, with A being an angle in quadrant 1, what is the value of cotA?

Sep 8, 2017

The value of $\cot A$ is $\sqrt{3}$.

#### Explanation:

We know that $\sin A = \frac{1}{2}$, and that $\cot A = \cos \frac{A}{\sin} A$. Also, ${\cos}^{2} x + {\sin}^{2} x = 1$. Accordingly:

${\left(\frac{1}{2}\right)}^{2} + {\cos}^{2} A = 1$

$\cos A = \frac{3}{4}$

$\cos A = \frac{\sqrt{3}}{2}$

Accordingly,

$\cot A = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

Hopefully this helps!

Sep 8, 2017

$\sqrt{3}$

#### Explanation:

$2 \sin A = 1$, then $\sin A = \frac{1}{2}$

it means, opposite side $= 1$ and hypotenuse $= 2$, therefore based on Pythagoras theorem, it adjacent = $\sqrt{{2}^{2} - {1}^{2}} = \sqrt{3}$

therefore

cot A = adjacent/opposite = $\frac{\sqrt{3}}{1} = \sqrt{3}$