Exercises

Here are some exercises to complete:

1.

Show that $\arcsin(x) + \arccos(x) = \pi/2$.

2.

Use your calculator to get approximate values for $\arctan(1.1)$,${\rm arccot}(1.1)$, ${\rm arcsec}(-4)$ and ${\rm arccsc}(-5)$. Don't forget to give answers in radians!

3.

Simplify $\cos(2\arctan(4))$ and $\sin(2\arctan(4))$. Draw the relevant triangles.

4.

By refering to the unit reference circle x² + y² = 1, simplify $\sec({\rm arccot}(-5))$.

5.

Simplify $\sin(2\arctan(x))$ and $\cos(2\arctan(x))$.

6.

Graph y = arcsin(sin(x)) for $x\in [-2\pi,2\pi]$. This is not the same as y = x!