Question

Determine o cosseno do arco de medida 255°.​

Answer 1

Explicação passo-a-passo:

• $\sf cos~255^{\circ}=-cos~(255^{\circ}-180^{\circ})$

$\sf cos~255^{\circ}=-cos~75^{\circ}$

• $\sf cos~(a+b)=cos~a\cdot cos~b-sen~a\cdot sen~b$

$\sf cos~75^{\circ}=cos~(45^{\circ}+30^{\circ})$

$\sf cos~75^{\circ}=cos~45^{\circ}\cdot cos~30^{\circ}-sen~45^{\circ}\cdot sen~30^{\circ}$

$\sf cos~75^{\circ}=\dfrac{\sqrt{2}}{2}\cdot\dfrac{\sqrt{3}}{2}-\dfrac{\sqrt{2}}{2}\cdot\dfrac{1}{2}$

$\sf cos~75^{\circ}=\dfrac{\sqrt{6}}{4}-\dfrac{\sqrt{2}}{4}$

$\sf cos~75^{\circ}=\dfrac{\sqrt{6}-\sqrt{2}}{4}$

Logo:

$\sf cos~255^{\circ}=-\left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)$

$\sf cos~255^{\circ}=\dfrac{\sqrt{2}-\sqrt{6}}{4}$