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

User Dave Gray
by
7.6k points

2 Answers

3 votes

Answer:

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


Explanation:

We want to find
arccos(-(1)/(2)).

This means we want to know the angle(s) for which cosine has a value of
-(1)/(2).

The basic acute angle that has a cosine of
(1)/(2) is 60°. But we want to know NEGATIVE
(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°

User Manoj Perumarath
by
8.2k points
1 vote

Answer:

120°


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.

User Ji Yalin
by
8.6k points

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