cos180/6+sin9*180/4-cos13*180/6

asked by guest
on Oct 19, 2024 at 12:29 pm



You asked:

Evaluate the expression: \(\frac{\cos\left( 180 \right)}{6} + \frac{\sin\left( 9 \right) \cdot 180}{4} - \frac{\cos\left( 13 \right) \cdot 180}{6}\)

MathBot Answer:

\[\frac{\cos\left( 180 \right)}{6} + \frac{\sin\left( 9 \right) \cdot 180}{4} - \frac{\cos\left( 13 \right) \cdot 180}{6} = - 30 \cos{\left(13 \right)} + \frac{\cos{\left(180 \right)}}{6} + 45 \sin{\left(9 \right)} \approx -8.77781495246981713304297728640131\]

\[\begin{aligned}\frac{\cos\left( 180 \right)}{6} + \frac{\sin\left( 9 \right) \cdot 180}{4} - \frac{\cos\left( 13 \right) \cdot 180}{6}& = \cos{\left(180 \right)} \cdot \frac{1}{6} + \sin{\left(9 \right)} \cdot \frac{180}{4} - \cos{\left(13 \right)} \cdot \frac{180}{6}\\& = \frac{1}{6} \cdot \cos{\left(180 \right)} + \sin{\left(9 \right)} \cdot \frac{180}{4} - \cos{\left(13 \right)} \cdot \frac{180}{6}\\& = \frac{1}{6} \cdot \cos{\left(180 \right)} + \sin{\left(9 \right)} \cdot 45 - \cos{\left(13 \right)} \cdot \frac{180}{6}\\& = \frac{1}{6} \cdot \cos{\left(180 \right)} + 45 \cdot \sin{\left(9 \right)} - \cos{\left(13 \right)} \cdot \frac{180}{6}\\& = \frac{1}{6} \cdot \cos{\left(180 \right)} + 45 \cdot \sin{\left(9 \right)} - \cos{\left(13 \right)} \cdot 30\\& = \frac{1}{6} \cdot \cos{\left(180 \right)} + 45 \cdot \sin{\left(9 \right)} - 30 \cdot \cos{\left(13 \right)}\\& = \left(45 \cdot \sin{\left(9 \right)} + \frac{1}{6} \cdot \cos{\left(180 \right)}\right) - 30 \cdot \cos{\left(13 \right)}\\& = -30 \cdot \cos{\left(13 \right)} + 45 \cdot \sin{\left(9 \right)} + \frac{1}{6} \cdot \cos{\left(180 \right)}\end{aligned}\]

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