All Tasks - Asymptote

This task type enables the user to insert a single fraction, either simple or mixed. Calculate the sum of $\frac{1}{5}$ and $\frac{14}{15}$. Divide the result by $\frac{3}{5}$ and finally subtract $\frac{11}{18}$. Insert the resulting mixed fraction below.

Now you are familiar with the basic principles of ASYMPTOTE and are ready to start working on a "real" learning graph. If you follow this tutorial further, we will introduce the variety of task formats that await you in ASYMPTOTE. If you want to finish the tutorial at this point, click the button in the upper right corner of the learning graph screen to return to the main menu.

How to use ASYMPTOTE? Here you will find the task, possibly enriched with an image. Below is the answer field for entering your calculated solution. But what is the solution here? Probably a hint can help you...

ASYMPTOTE is a free learning environment that enables adaptive and synchronous online teaching. We explain how to use the app in this learning graph. Enjoy!

Find the values of $ \alpha$ and $\beta$ given by \[\alpha=\arccos\left(-\frac{1}{2}\right)\] and \[\beta=\arctan\left(-\frac{\sqrt 3}{3}\right)\]

Let $f(x)=\text{arccot}(\alpha-5x)-\pi,\quad \alpha\in\mathbb{R}$. If $f'(1)=1$ then $\alpha$ is equal to