Question

alguien me ayuda por favor​

Answer 1

Explicación paso a paso:

a)

$sen( \alpha ) = \frac{ \sqrt{2} }{2} \to \: \alpha = {45}^{0}$

b)

$2cos(2 \theta) - \sqrt{3} = 0$

$cos(2 \theta) = \frac{ \sqrt{3} }{2}$

$arccos( \frac{ \sqrt{3} }{2} ) = {30}^{0}$

$2\theta = {30}^{0} \to \: \theta = {15}^{0}$

c)

$\sqrt{3} tan( \frac{1}{3} t) = 1$

$tan( \frac{1}{3} t) = \frac{1}{ \sqrt{3} }$

$arctan( \frac{1}{ \sqrt{3} } ) = {60}^{0}$

$\frac{1}{3} t = {60}^{0} \to \: t = {180}^{0}$

d)

$2sen(3 \theta) + \sqrt{2} = 0$

$sen( 3\theta) = - \frac{ \sqrt{2} }{2}$

$arcsen( - \frac{ \sqrt{2} }{2} ) = - {45}^{0}$

$3 \theta = - {45}^{0} \to \: \theta = - {15}^{0}$

e)

$sen( \theta + \frac{\pi}{2} ) = \frac{1}{2}$

$sen( \frac{2 \theta + \pi}{2} ) = \frac{1}{2}$

$\pi = {180}^{0}$

$arcsen( \frac{1}{2} ) = {30}^{0}$

$2 \theta + {180}^{0} =2( {30}^{0} )$

$2 \theta = - {120}^{0} \to \: \theta = - {60}^{0}$

f)

$cos( \alpha - \frac{\pi}{3} ) = - 1$

$\frac{\pi}{3} = \frac{ {180}^{0} }{3} = {60}^{0}$

$arccos( - 1) = {180}^{0}$

$\alpha - ( {60}^{0} ) = {180}^{0} \to \: \alpha = {240}^{0}$