15$sin^{2}$(74.5)-26cos(74.5)-23

asked by guest
on Nov 24, 2024 at 12:07 pm



You asked:

Evaluate the expression: \(15 {\sin\left( 74.5 \right)}^{2} - 26 \cdot \cos\left( 74.5 \right) - 23\)

MathBot Answer:

\[15 {\sin\left( 74.5 \right)}^{2} - 26 \cdot \cos\left( 74.5 \right) - 23 = -23 - 26 \cos{\left(\frac{149}{2} \right)} + 15 \sin^{2}{\left(\frac{149}{2} \right)} \approx -30.01995382762100168931672394730318\]

\[\begin{aligned}15 {\sin\left( 74.5 \right)}^{2} - 26 \cdot \cos\left( 74.5 \right) - 23& = 15 \cdot \sin^{2}{\left(74 + \frac{5}{10} \right)} - 26 \cdot \cos{\left(74 + \frac{5}{10} \right)} - 23\\& = 15 \cdot \sin^{2}{\left(74 + \frac{1}{2} \right)} - 26 \cdot \cos{\left(74 + \frac{5}{10} \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(74 + \frac{5}{10} \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(74 + \frac{1}{2} \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(\frac{149}{2} \right)} - 23\\& = \left(-26 \cdot \cos{\left(\frac{149}{2} \right)} + 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)}\right) - 23\\& = -23 - 26 \cdot \cos{\left(\frac{149}{2} \right)} + 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)}\end{aligned}\]

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