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.