Answer:
see explanation
Step-by-step explanation:
3tanx - 2 = 4cos35.3° ( add 2 to both sides )
3tanx = 4cos35.3° + 2 ( divide both sides by 3 )
tanx = [tex]\frac{4cos35.3+2}{3}[/tex] ≈ 1.75485
(b)
x = [tex]tan^{-1}[/tex] (1.75485) ≈ 60.3° ( to 1 dec. place )
The value of [tex]tan x[/tex] is 1.758 and value of x is 60.4° .
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
The basic trigonometric ratios formulas are given below,
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
According to the question
The trigonometric equation:
[tex]3 tan x - 2 = 4 cos (35.3)[/tex]
a) To Find tan x
Solving trigonometric equation:
[tex]3 tan x - 2 = 4 cos (35.3)[/tex]
As Cos(35.3°) = 0.8192
Therefore,
[tex]3 tan x - 2 = 4 * 0.8192[/tex]
[tex]3 tanx = 5.2768[/tex]
[tex]tan x = 1.758[/tex]
b) the value of x in degree
[tex]tan x = 1.758[/tex]
therefore ,
x = [tex]tan^{-1} 1.758[/tex]
x = 60.4°
Hence, The value of [tex]tan x[/tex] is 1.758 and value of x is 60.4° .
To know more about trigonometric ratios here:
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