Question

How to find the value of θ when given sin θ = 1/3.

a) θ = arcsin(1/3)
b) θ = arccos(1/3)
c) θ = arctan(1/3)
d) θ = arccot(1/3)

Answer 1

The value of θ when given sin θ = 1/3 is found using the inverse sine function, so the answer is θ = arcsin(1/3).

Step-by-step explanation:

To find the value of θ when given sin θ = 1/3, you would use the inverse sine function, or arcsin. This is because the sine function gives the ratio of the opposite side to the hypotenuse in a right-angled triangle, and the inverse sine function, also known as arcsin, gives the angle whose sine is a given number.

Therefore, the correct answer to find the value of θ is:

• θ = arcsin(1/3)

The other options provided such as arccos, arctan, or arccot would not give the correct angle for the specified sine value, as each corresponds to the inverse function of cosine, tangent, and cotangent respectively.