Inverse Cosine (C)

For every real number $x\in[-1,1]$ there is an angle between 0 and 180 degrees, or, in radian measure, between and $\pi$ radians, whose cosine is x. This angle is denoted by $\arccos(x)$, called the arc cosine or inverse cosine. Most calculators will return approximate values of $\arccos(x)$ for given values of x. Some the important values, are given in the following table. When using a calculator, be sure to check whether it is set in degree or radian mode.

$$\begin{array} {ccc} x & \arccos(x){\rm \;in\;radians} & \ar... ...2 & \pi/4 & 45\\ \sqrt{3}/2 & \pi/6 & 30\\ 1 & 0 & 0\end{array}$$

Exercises Give the following angles exactly in radians and degrees if possible. If not, give their decimal approximations to 5 decimal places in radians and to the nearest second if in degrees.

1.

$\arccos(1/2)$;

2.

$\arccos(1/3)$;

3.

$\arccos(-1/3)$