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4 votes
Which of the following is the value of cos⁻¹ (√2/2) = θ

A. /3
B. /6
C. /4
D. /2

1 Answer

3 votes

Final answer:

The value of cos⁻¹ (√2/2) is θ = π/4 or 45°.

Step-by-step explanation:

The value of cos⁻¹ (√2/2) is θ = π/4 or 45°. Therefore, the correct answer is C. /4.

The expression

cos

1

(

2

/

2

)

cos

−1

(

2

/2) represents the inverse cosine function, also denoted as arccosine, and is commonly used to find an angle (

θ) whose cosine is equal to a given value. In this case,

cos

1

(

2

/

2

)

cos

−1

(

2

/2) corresponds to an angle

θ where the cosine is equal to

2

/

2

2

/2.

The value

2

/

2

2

/2 is commonly associated with the cosine of 45 degrees or

/

4

π/4 radians. Therefore,

cos

1

(

2

/

2

)

cos

−1

(

2

/2) would be equal to 45 degrees or

/

4

π/4 radians.

In summary, the value of

cos

1

(

2

/

2

)

cos

−1

(

2

/2) is an angle

θ equal to 45 degrees or

/

4

π/4 radians. This angle is known for having a cosine value of

2

/

2

2

/2, and the arccosine function helps identify this angle given the cosine value.

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