Question

What is the value of arccos (-1/2)

Answer 1

Answer:

120° & 240° (given the angles are between 0° and 360°)

Step-by-step explanation:

We want to find $arccos(-\frac{1}{2})$.

This means we want to know the angle(s) for which cosine has a value of $-\frac{1}{2}$.

The basic acute angle that has a cosine of $\frac{1}{2}$  is 60°. But we want to know NEGATIVE $\frac{1}{2}$. So in which quadrants is cosine negative? Second and Third

• The rule to find 2nd quadrant angle with known acute angle is: 180 - α
• The rule to find 3rd quadrant angle with known acute angle is: 180 + α

Where α is the basic acute angle (in our case it is 60°)

So 2nd quadrant angle is 180 - 60 = 120°

and 3rd quadrant angle is 180 + 60 = 240°

Answer 2

Answer:

120°

Step-by-step explanation:

arccos means the inverse of cosine.

arccos (-1/2) ⇒ We can rewrite this equation as;

cosФ = 1/2 Find the value of  Ф.

Ф = arccos (-1/2) ⇒ This can be calculated directly from the calculator.

arccos (-1/2) = 120°

or arccos (-1/2) = (180 + 60)

                         = 240°

You can have more than one value of arccos (-1/2) since the cosine is negative in the second and third quadrant.