Question

Calcule o valor da expressão sen 15° + cos 75°. Adote a raiz quadrada de 2 igual a 1,41 e a raiz quadrada de 6 igual a 2,45.
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Answer 1

$\boxed{\begin{array}{l}\sf sen(15^\circ)=cos(90^\circ-15^\circ)=cos(75^\circ)\\\sf sen(15^\circ)+cos(75^\circ)=2\cdot cos(75^\circ)\\\sf cos(75^\circ)=cos(30^\circ+45^\circ)\\\sf cos(75^\circ)=cos(30^\circ)\cdot cos(45^\circ)-sen(30^\circ)\cdot sen(45^\circ)\\\sf cos(75^\circ)=\dfrac{\sqrt{3}}{2}\cdot\dfrac{\sqrt{2}}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt{2}}{2}\\\\\sf cos(75^\circ)=\dfrac{\sqrt{6}}{4}-\dfrac{\sqrt{2}}{4}=\dfrac{\sqrt{6}-\sqrt{2}}{4}\\\\\sf cos(75^\circ)=\dfrac{2,45-1,41}{4}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf cos(75^\circ)=\dfrac{1,04}{2}\\\\\sf cos(75^\circ)=0,26\\\sf sen(15^\circ)+cos(75^\circ)=2 cos(75^\circ)\\\sf sen(15^\circ)+cos(75^\circ)=2\cdot0,26\\\sf sen(15^\circ)+cos(75^\circ)=0,52\end{array}}$