Question

sem usar calculadora simplifique as expressões


a) sen(x +300) - cos (x-150)

b)
$\frac{sen(180 - \alpha )}{2sen(90 - \alpha )}$
​

Answer 1

Resposta:

a) (senx - √3cosx)/2

b) 1/2 tgα

Explicação passo-a-passo:

sen300° = -sen(360°-300°) = -sen60° = -√3/2

cos(300°) = cos(360°-300°) = cos60° = 1/2

sen150° = sen(180°-150°) = sen30° = 1/2

cos150° = -cos(180°-150°) = -cos30° = -√3/2

sen(a+b) = senacosb + senbcosa

a)sen(x + 300°) = sen(x + 300°) = senxcos300° + sen300°cosx =

senx.1/2  -√3/2cosx = (senx - √3cosx)/2

b) a) sen(180° - α) = sen(180° -(180° -α)) = senx

2sen(90° - α) = 2cosα

sen(180° - α) :2cos(90° - α) = senα : 2cosα =1/2 tgα