Question

pls solve the following math from trigonometry ​

Answer 1

Step-by-step explanation:

$\tan(2x) = 1.5$

Take the arc tangent,

$\tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5)$

$2x = 56.3$

$x = 28.15$

b.

$(3 \cos(x) + 1)(2 \cos(x) + 3) = - 2$

$6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2$

$6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0$

$6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0$

$6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0$

$(6 \cos(x) + 5)( \cos(x) + 1) = 0$

Set each factor equal to zero.

$6 \cos(x) + 5 = 0$

$6 \cos(x) = - 5$

$\cos(x) = - \frac{5}{6}$

$x = \cos {}^{ - 1} ( \frac{5}{6} )$

$x = 146.4$

For the second factor,

$\cos(x) + 1 = 0$

$\cos(x) = - 1$

$x = 180$

So the answer for the second one is

146.4 and 180.