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2. Given that x is an acute angle and that 3 tan x - 2 = 4 cos 35.3°
calculate: a) tan x
b) the value of x in degrees correct to 1 d.p.​

Sagot :

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° .

What is trigonometric ratio?

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:

https://brainly.com/question/1201366

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