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QuestionFind the decimal approximation of sin⁡61∘6′\sin 61^{\circ} 6^{\prime}. Round to eight decimal places.

Studdy Solution

STEP 1

Assumptions1. We are asked to find a decimal approximation for the trigonometric function sin⁡61∘6′\sin61^{\circ}6^{\prime} . We are using a calculator that can compute trigonometric functions3. We are rounding our answer to eight decimal places as needed

STEP 2

First, we need to convert the angle from degrees and minutes to decimal degrees. We can do this using the formulaDegrees=degrees+minutes60Degrees = degrees + \frac{minutes}{60}

STEP 3

Now, plug in the given values for degrees and minutes to convert the angle to decimal degrees.
Degrees=61+660Degrees =61 + \frac{6}{60}

STEP 4

Calculate the decimal degree value.
Degrees=61+660=61.1∘Degrees =61 + \frac{6}{60} =61.1^{\circ}

STEP 5

Now that we have the angle in decimal degrees, we can find the sine of this angle using a calculator.
sin⁡61.1∘\sin61.1^{\circ}

STEP 6

Use a calculator to find the sine of the angle. Make sure your calculator is set to degrees mode.
sin⁡61.1∘≈0.8746197071\sin61.1^{\circ} \approx0.8746197071

STEP 7

Finally, round the result to eight decimal places as needed.
sin⁡61.1∘≈0.87461971\sin61.1^{\circ} \approx0.87461971So, sin⁡61∘6′≈0.87461971\sin61^{\circ}6^{\prime} \approx0.87461971.

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