Trigonometric Roots and Substitutions: Solving Equations in Terms of Pi

  • Thread starter Gughanath
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In summary, The roots of the equation 2x^3-5x^2-4x+3=0 are x=-1, 3, and 1. However, when substituting x=cost, the equation 2cos^3t-5cos^2t-4cost+3=0 must be solved for 0<t<2π, giving the answer in radians in terms of π. There are multiple solutions for cos(t)=-1 and cos(t)=1/2, and if complex numbers are allowed, cos(t)=3 can also be solved. It should also be noted that one of the solutions for x does not work in the original equation.
  • #1
Gughanath
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The first part of this question was to find the roots of the equation 2x^3-5x^2-4x+3=0 i got x=-1, 3, and 1.

but then the second part completely confused me
b) Hence, by substituting x=cost solve the equation 2cos^3t-5cos^2t -4cost+3=0 for 0<t<2"pie", giving your answer in radians in terms of pie.

PLEASE HELP! :confused: :confused: :confused:
 
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  • #2
Can you solve cos(t)=-1?

Oh, you've solve the cubic equation wrong, 1 of the solutions for x does not work.
 
Last edited:
  • #3
Gughanath said:
giving your answer in radians in terms of pie.

PLEASE HELP!

The roots are : x=-1,3,1/2.

Just solve : cos(t)=-1 and cos(t)=1/2...this gives of course an infinity of real answers...

If you allow complex numbers, then you can solve cos(t)=3...

NB : You're great, with your help I know how the english pronounciation of [tex]\pi[/tex] double explain it's origin :biggrin:
 

FAQ: Trigonometric Roots and Substitutions: Solving Equations in Terms of Pi

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Why is trigonometry important?

Trigonometry is used in a variety of fields, such as engineering, physics, and astronomy, to solve problems involving angles and distances. It also has practical applications in navigation, surveying, and construction.

What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent, which represent the ratios of the sides of a right triangle.

What is the unit circle?

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is used in trigonometry to relate the values of the trigonometric functions to the coordinates of points on the circle.

How can I use trigonometry in real life?

Trigonometry is used in a variety of real-life applications, such as designing buildings, creating maps, and analyzing sound waves. It can also be used to solve problems involving angles and distances, such as finding the height of a tree or the distance between two points on a map.

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