Question

Pls solve the following math from trigonometry ​

Answer 1

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) = - (5)/(6)`

`x = \cos {}^( - 1) ( (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.