Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.