sin β = -0.6 for all 0 ≤ β ≤ 2π
This statement is false.
The sine function can only output values between -1 and 1. Therefore, there is no value of β between 0 and 2π that would yield a sine value of -0.6.
Perhaps the intended statement was "there exists β between 0 and 2π such that sin β = -0.6." This statement would be true, as there are values of β that would yield a sine value of -0.6, such as β ≈ 5.666.
culture in the tall woman and her short husband
"The Tall Woman and Her Short Husband" is a story by Feroz Ahmed Jami that portrays the cultural norms and values of Bangladeshi society. In the story, the main character, the wife, is described as being tall and having a very fair complexion, while her husband is short and dark-skinned. This physical difference between them creates a tension in their marriage because in their society, it is expected that a husband should be taller and fairer than his wife.
The story depicts the cultural belief that physical appearance, especially height and skin color, is a crucial factor in determining social status and desirability. This belief extends to the families of the couple as well, who are concerned about their reputation in society due to the husband's physical shortcomings.
Another aspect of Bangladeshi culture that is portrayed in the story is the importance of family and community. The husband's family feels ashamed of his height and dark skin, and they criticize him for marrying a taller and fairer woman. The wife's family is more accepting of the situation, but they still pressure her to find a taller and fairer husband.
Overall, "The Tall Woman and Her Short Husband" illustrates the cultural norms and expectations within Bangladeshi society, specifically regarding physical appearance and family reputation.
To find the values of β for which sin β = -0.6 and 0 ≤ β ≤ 2π, you can follow these steps:
Step 1: Determine the reference angle
To find the reference angle, take the inverse sine (or arcsin) of the given value of -0.6 using a scientific calculator. The arcsin of -0.6 is approximately -0.6435 radians.
Step 2: Find the principal angle
The principal angle is the angle in the first quadrant that has the same sine value as the given value (-0.6). In this case, the principal angle is approximately 0.6435 radians.
Step 3: Determine the other angles
Since the sine function is negative in the third and fourth quadrants, you need to find the other angles that have the same sine value (-0.6) by adding or subtracting the reference angle or the principal angle.
In the third quadrant (where sin is negative), subtract the reference angle from π radians (180 degrees). Thus, the angle β1 in the third quadrant is approximately π - 0.6435 = 2.4981 radians.
In the fourth quadrant (where sin is negative), subtract the reference angle from 2π radians (360 degrees). Thus, the angle β2 in the fourth quadrant is approximately 2π - 0.6435 = 5.6396 radians.
Step 4: Round the angles (if necessary)
If you need the angles in a specific format (such as degrees or a certain number of decimal places), you can round the angles to the desired precision.
In summary, the angles β that satisfy sin β = -0.6 and 0 ≤ β ≤ 2π are approximately:
-0.6435 radians (principal angle)
2.4981 radians (third quadrant angle)
5.6396 radians (fourth quadrant angle)