QuestionCalculate the decimal approximation for $\sin 44^{\circ} 48^{\prime}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the angle in degrees and minutes, where1 degree equals60 minutes. . We are asked to find the decimal approximation of the sine of this angle.
3. We can use a scientific calculator to find the decimal approximation.

STEP 2

First, we need to convert the angle from degrees and minutes to decimal degrees. We can do this by dividing the minutes by60 and adding the result to the degrees.
$Degrees = Degrees + \frac{Minutes}{60}$

STEP 3

Now, plug in the given values for the degrees and minutes to convert the angle to decimal degrees.
$Degrees =44^{\circ} + \frac{48^{\prime}}{60}$

STEP 4

Calculate the decimal degree value.
$Degrees =44^{\circ} + \frac{48^{\prime}}{60} =44.8^{\circ}$

STEP 5

Now that we have the angle in decimal degrees, we can find the sine of this angle using a scientific calculator. Ensure that your calculator is set to degrees mode.
$\sin(44.8^{\circ})$

STEP 6

Calculate the sine of the angle.
$\sin(44.8^{\circ}) \approx0.7071$ The decimal approximation for the sine of $44^{\circ}48^{\prime}$ is approximately0.7071.

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