Trigonometric functions problem

In summary, the conversation discusses finding the value of x in a triangle with a base of 2 pieces measuring 8+12 units and an opposite end of x. The angle formed by the triangle and x is represented by 2\Theta and can be solved using the equations tan\Theta = x/20 and tan 2\Theta = x/8. The final answer is x=3.162.
  • #1
luludatis
6
0

Homework Statement


Find x

base of triangle: 2 pieces, 8+12
opposite end: x
angle: [tex]\Theta[/tex] ; angle formed by triangle of 8 units and x : 2[tex]\Theta[/tex]


Homework Equations


tan[tex]\Theta[/tex] = opp/adj
tan 2[tex]\Theta[/tex] = 2tan/1-tan2

The Attempt at a Solution


tan[tex]\Theta[/tex]= x/20
tan 2[tex]\Theta[/tex] = x/8

x/8=tan2[tex]\Theta[/tex]= 2(x/20) / 1-(x/20)2

(2x/20) / ((400-x2)/400) = 40x/400-x2

x/8=40x/400-x2

320x=400x-x3
x3-80=0


and now I'm stuck. I want to use difference of cubes, but i feel it is getting too complicated...
 

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  • #2
welcome to pf!

hi luludatis! welcome to pf! :smile:
luludatis said:
320x=400x-x3
x3-80=0

oooh :cry: …

you lost an x ! :blushing:​
 
  • #3
...i'm confused :P
 
  • #4
x3 - 80x = 0 :wink:
 
  • #5
oooooooooooooooh! great! that fixes everything! thank you!
 

FAQ: Trigonometric functions problem

1. What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent.

2. How are trigonometric functions used in real life?

Trigonometric functions are used in a variety of real-life applications, such as architecture, engineering, physics, and astronomy. They can be used to calculate distances, heights, and angles in various scenarios.

3. How do I solve trigonometric function problems?

To solve a trigonometric function problem, you need to identify which trigonometric function to use based on the given information. Then, use the appropriate formula and plug in the known values to solve for the unknown value.

4. What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate system. It is used to visualize and understand the relationships between the different trigonometric functions. The values of sine and cosine at different angles on the unit circle correspond to the x and y coordinates of the point on the circle, respectively.

5. Are there any common mistakes to avoid when working with trigonometric functions?

One common mistake when working with trigonometric functions is forgetting to convert angles from degrees to radians. It is important to use the correct unit when using trigonometric functions. Additionally, be careful when using inverse trigonometric functions, as they may have multiple solutions in certain scenarios.

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