Question

1) O valor de cos 400° é igual a:
a) cos 40°
Ob) - cos 40°
c) sen 40°
d) - sen 40°​

Answer 1

$\large \boxed{\boxed{{\tt =cos \left(40^{\circ \:}\right) }}}$

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$\sf cos \left(400^{\circ \:}\right)\\\\\\\sf \displaystyle cos \left(400^{\circ \:}\right)=cos \left(\frac{18+2}{9}180^{\circ \:}\right)=cos \left(\left(\frac{18}{9}+\frac{2}{9}\right)180^{\circ \:}\right)=cos \left(360^{\circ \:}+\frac{2}{9}180^{\circ \:}\right)\\\\\\\sf =cos \left(360^{\circ \:}+\frac{2}{9}180^{\circ \:}\right)\\\\\\\sf {Utilize\:a\:periodicidade\:de\:}cos :\quad cos \left(x+360^{\circ \:}\cdot \:k\right)=cos \left(x\right)$

$\sf \displaystyle cos \left(360^{\circ \:}+\frac{2}{9}180^{\circ \:}\right)=cos \left(\frac{2}{9}180^{\circ \:}\right)\\\\\\\\\sf =cos \left(\frac{2}{9}180^{\circ \:}\right)\\\\\\\\\large \to \boxed{\boxed{{\tt =cos \left(40^{\circ \:}\right) }}}$

$\tt Alterna\to A)$