If = sin-10.398, then =_____o_____' _____". Round to the nearest second.

Do you mean

sin-1(0.398)
= ? ° ? ' ? "
= 23.45320822°
multiply the decimal part by 60
=23°27.19249'
multiply the decimal part by 60
=23°-27'-11.55" (approx.)
=23°-27'-12" (nearest second)

Yes. Thank you.

You're welcome!

To find the value of θ, given that sinθ = -0.398, we need to use the inverse sine function (sin^(-1)) or arcsine. The problem states that θ is given in degrees and minutes.

1. Start by using a scientific calculator or a trigonometric table that provides the inverse sine function (sin^(-1)).
2. Enter -0.398 into the calculator or find -0.398 in the table.
3. Take the inverse sine (sin^(-1)) of -0.398.
4. The calculator or table will give you the result in radians. We want the result in degrees and minutes, so we need to convert it.

To convert the result from radians to degrees:
1. Multiply the result by 180/π to convert it from radians to degrees. π (pi) is approximately 3.14159.

Now, let's solve for θ:

Using a calculator or table: sin^(-1)(-0.398) = -0.4081 radians
Converting radians to degrees: -0.4081 * (180/π) = -23.374 degrees
Since the question requires the answer to be rounded to the nearest second, we'll take into account the decimal portion of the degrees.

To find the minutes:
1. Multiply the decimal part of the degrees by 60.
2. Round this result to the nearest whole number to get the minutes.

-0.374 * 60 = -22.44
Rounded to the nearest whole number, the minutes would be -22.

Therefore, θ = -23° - 22' (rounded to the nearest second).