cos 105^{circ}

Question

cos 105^{circ}

Accepted Answer

Step:1 ：Break down 105 degrees into the sum of two known angles: (105^circ = 45^circ + 60^circ)Step:2 ：Use the sum of angles formula for cosine: (cos (A + B) = cos A cos B - sin A sin B)Step:3 ：Calculate (cos (45^circ + 60^circ) = cos 45^circ cos 60^circ - sin 45^circ sin 60^circ)Step:4 ：Plug in the values: (frac{sqrt{2}}{2} cdot frac{1}{2} - frac{sqrt{2}}{2} cdot frac{sqrt{3}}{2})Step:5 ：Simplify the expression: (-frac{sqrt{6} + sqrt{2}}{4})Step:6 ：(boxed{cos 105^circ approx -0.2588})

Answer

Step: 1 ：Break down 105 degrees into the sum of two known angles: (105^circ = 45^circ + 60^circ)Step: 2 ：Use the sum of angles formula for cosine: (cos (A + B) = cos A cos B - sin A sin B)Step: 3 ：Calculate (cos (45^circ + 60^circ) = cos 45^circ cos 60^circ - sin 45^circ sin 60^circ)Step: 4 ：Plug in the values: (frac{sqrt{2}}{2} cdot frac{1}{2} - frac{sqrt{2}}{2} cdot frac{sqrt{3}}{2})Step: 5 ：Simplify the expression: (-frac{sqrt{6} + sqrt{2}}{4})Step: 6 ：(boxed{cos 105^circ approx -0.2588})

$\cos 105^{\circ}$

Answer

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