Nena752idn
Answered

Explore IDNLearn.com to discover insightful answers from experts and enthusiasts alike. Discover detailed answers to your questions with our extensive database of expert knowledge.

Hey! Can someone please answer this?

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

#SPJ2

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.