15sin2sin^{2}(74.5)-26cos(74.5)-23

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



You asked:

Evaluate the expression: 15sin⁡(74.5)2−26cos⁡(74.5)−2315 {\sin\left( 74.5 \right)}^{2} - 26 \cos\left( 74.5 \right) - 23

MathBot Answer:

15sin⁡(74.5)2−26cos⁡(74.5)−23=−23−26cos⁡(1492)+15sin⁡2(1492)≈−30.0199538276210016893167239473031815 {\sin\left( 74.5 \right)}^{2} - 26 \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

15sin⁡(74.5)2−26cos⁡(74.5)−23=15⋅sin⁡2(74+510)−26⋅cos⁡(74+510)−23=15⋅sin⁡2(74+12)−26⋅cos⁡(74+510)−23=15⋅sin⁡2(1492)−26⋅cos⁡(74+510)−23=15⋅sin⁡2(1492)−26⋅cos⁡(74+12)−23=15⋅sin⁡2(1492)−26⋅cos⁡(1492)−23=(−26⋅cos⁡(1492)+15⋅sin⁡2(1492))−23=−23−26⋅cos⁡(1492)+15⋅sin⁡2(1492)\begin{aligned}15 {\sin\left( 74.5 \right)}^{2} - 26 \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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