Given that sin theta=0.488, find theta in correct to nearest minute given that theta is acute
since sin 29.209° = 0.488,
θ = 29.209°
I'll leave it to you to convert the .209° to minutes
To find the value of theta, we can use the inverse sine function (also known as arcsin or sin^(-1)). The inverse sine function gives us the angle whose sine is a given value.
Let's use the arcsin function to find theta:
arcsin(0.488) ≈ 28.21
The result, 28.21, is in radians. However, since you want the answer in degrees and minutes, we need to convert it.
To convert radians to degrees, we can use the conversion factor: 180°/π radians.
theta ≈ 28.21 × (180°/π) ≈ 1617.9°
Now, we need to convert degrees to degrees and minutes.
Since 1 degree = 60 minutes,
1617.9° × 60 = 97074 minutes
Rounding 97074 to the nearest minute, we get:
theta ≈ 97074 minutes
Therefore, the value of theta, to the nearest minute, is 97074 minutes.