QuestionEvaluate: $\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}$ . Round to four decimal places.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\sin164^{\circ}48^{\prime} \cos15^{\circ}12^{\prime}+\cos164^{\circ}48^{\prime} \sin15^{\circ}12^{\prime}$ to evaluate. . We are using a calculator to evaluate the expression.
3. The trigonometric functions sine and cosine are in degrees, not radians.
4. The prime symbol (') represents minutes, where1 degree =60 minutes.
5. We are rounding the result to four decimal places.

STEP 2

First, we need to convert the degrees and minutes into decimal degrees. This can be done by dividing the minutes by60 and adding the result to the degrees.
$164^{\circ}48^{\prime} =164 + \frac{48}{60}$ $15^{\circ}12^{\prime} =15 + \frac{12}{60}$

STEP 3

Now, plug in the given values for degrees and minutes to calculate the decimal degrees.
$164^{\circ}48^{\prime} =164 + \frac{48}{60} =164.8^{\circ}$ $15^{\circ}12^{\prime} =15 + \frac{12}{60} =15.2^{\circ}$

STEP 4

Now that we have the decimal degrees, we can substitute these values into the original expression.
$\sin164.8^{\circ} \cos15.2^{\circ}+\cos164.8^{\circ} \sin15.2^{\circ}$

STEP 5

Next, use a calculator to evaluate the sine and cosine of the decimal degrees.
$\sin164.8^{\circ} = -0.9781$ $\cos164.8^{\circ} = -0.2079$ $\sin15.2^{\circ} =0.2618$ $\cos15.2^{\circ} =0.9651$

STEP 6

Substitute these values back into the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.2618$

STEP 7

Finally, use a calculator to evaluate the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.261 = -0.9446$ The result is -0.9446, rounded to four decimal places.

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QuestionEvaluate: $\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}$ . Round to four decimal places.

Studdy Solution

STEP 1

STEP 2

First, we need to convert the degrees and minutes into decimal degrees. This can be done by dividing the minutes by60 and adding the result to the degrees.
$164^{\circ}48^{\prime} =164 + \frac{48}{60}$ $15^{\circ}12^{\prime} =15 + \frac{12}{60}$

STEP 3

Now, plug in the given values for degrees and minutes to calculate the decimal degrees.
$164^{\circ}48^{\prime} =164 + \frac{48}{60} =164.8^{\circ}$ $15^{\circ}12^{\prime} =15 + \frac{12}{60} =15.2^{\circ}$

STEP 4

Now that we have the decimal degrees, we can substitute these values into the original expression.
$\sin164.8^{\circ} \cos15.2^{\circ}+\cos164.8^{\circ} \sin15.2^{\circ}$

STEP 5

Next, use a calculator to evaluate the sine and cosine of the decimal degrees.
$\sin164.8^{\circ} = -0.9781$ $\cos164.8^{\circ} = -0.2079$ $\sin15.2^{\circ} =0.2618$ $\cos15.2^{\circ} =0.9651$

STEP 6

Substitute these values back into the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.2618$

STEP 7

Finally, use a calculator to evaluate the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.261 = -0.9446$ The result is -0.9446, rounded to four decimal places.

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QuestionEvaluate: sin⁡164∘48′cos⁡15∘12′+cos⁡164∘48′sin⁡15∘12′\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}sin164∘48′cos15∘12′+cos164∘48′sin15∘12′. Round to four decimal places.

Studdy Solution

STEP 1

STEP 2

STEP 3

STEP 4

Now that we have the decimal degrees, we can substitute these values into the original expression.sin⁡164.8∘cos⁡15.2∘+cos⁡164.8∘sin⁡15.2∘\sin164.8^{\circ} \cos15.2^{\circ}+\cos164.8^{\circ} \sin15.2^{\circ}sin164.8∘cos15.2∘+cos164.8∘sin15.2∘

STEP 5

STEP 6

Substitute these values back into the expression.−0.9781×0.9651+−0.2079×0.2618-0.9781 \times0.9651 + -0.2079 \times0.2618−0.9781×0.9651+−0.2079×0.2618

STEP 7

Finally, use a calculator to evaluate the expression.−0.9781×0.9651+−0.2079×0.261=−0.9446-0.9781 \times0.9651 + -0.2079 \times0.261 = -0.9446−0.9781×0.9651+−0.2079×0.261=−0.9446The result is -0.9446, rounded to four decimal places.

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QuestionEvaluate: $\sin 164^{\circ} 48^{\prime} \cos 15^{\circ} 12^{\prime} + \cos 164^{\circ} 48^{\prime} \sin 15^{\circ} 12^{\prime}$ . Round to four decimal places.

Now that we have the decimal degrees, we can substitute these values into the original expression.
$\sin164.8^{\circ} \cos15.2^{\circ}+\cos164.8^{\circ} \sin15.2^{\circ}$

Substitute these values back into the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.2618$

Finally, use a calculator to evaluate the expression.
$-0.9781 \times0.9651 + -0.2079 \times0.261 = -0.9446$ The result is -0.9446, rounded to four decimal places.