nena752
Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts 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

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.