Questions: 315,09 · cos 77° 1,3' = 315,09 · cos 257° 1,3' =

315,09 · cos 77° 1,3' = 315,09 · cos 257° 1,3' =
Transcript text: $\begin{array}{l}315,09 \cdot \cos 77^{\circ} 1,3^{\prime}= \\ 315,09 \cdot \cos 257^{\circ} 1,3^{\prime}=\end{array}$
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Solution

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Solution Steps

To solve the given trigonometric expressions, we need to convert the angles from degrees and minutes to decimal degrees, then use the cosine function to find the values. The cosine function in Python's math library requires angles in radians, so we will also convert the angles from degrees to radians before calculating the cosine.

Step 1: Calculate \( \cos(77^\circ 1.3') \)

First, we convert \( 77^\circ 1.3' \) to decimal degrees: \[ 77 + \frac{1.3}{60} = 77.0216667^\circ \] Next, we calculate the cosine: \[ \cos(77.0216667^\circ) \approx 0.2246 \]

Step 2: Calculate the first expression

Now, we compute the first expression: \[ 315.09 \cdot \cos(77^\circ 1.3') \approx 315.09 \cdot 0.2246 \approx 70.7637 \]

Step 3: Calculate \( \cos(257^\circ 1.3') \)

Next, we convert \( 257^\circ 1.3' \) to decimal degrees: \[ 257 + \frac{1.3}{60} = 257.0216667^\circ \] Then, we calculate the cosine: \[ \cos(257.0216667^\circ) \approx -0.2246 \]

Step 4: Calculate the second expression

Now, we compute the second expression: \[ 315.09 \cdot \cos(257^\circ 1.3') \approx 315.09 \cdot (-0.2246) \approx -70.7637 \]

Final Answer

The results for the two expressions are: \[ \boxed{70.7637} \] and \[ \boxed{-70.7637} \]

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