2 Trig Equations Answer one or the other is fine

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In summary, the first problem involves solving the equation tan(x)=3 tan(x/2) within the given domain of 0<x<2pi. The second problem involves using an addition theorem to find the values of sin(alpha+beta) that satisfy the equation sin3xcosx+cos3xsinx=1 within the given domain. Possible methods for solving these equations include graphical methods and using trigonometric tables.
  • #1
BuffaloSoulja
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Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
 
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  • #2
Hiya
what methods have you tried? A graphical method often leads to insights - plot the 2 graphs and see where they intersect. Then look for the reasons why and hey presto! the answer.
 
  • #3
My old (1954) CRC Mathematics Tables book has exact trig relationships for tan x, tan 2x, and tan 3x. Also sin x, sin 2x, sin 3x, sin 4x and sin 5x. Also cosines. (page 344)
Bob S
 
  • #4
BuffaloSoulja said:
Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
Hello BuffaloSoulja
The second looks very much like an addition theorem:
sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)
find alpha and beta and make the solution.
greetings Janm
 

1. What are 2 trig equations?

2 trig equations are mathematical expressions that involve trigonometric functions such as sine, cosine, and tangent. They are used to solve problems related to angles and triangles.

2. What is the purpose of solving 2 trig equations?

The purpose of solving 2 trig equations is to find the values of unknown angles or side lengths in a triangle. This can help in solving real-world problems involving navigation, construction, and more.

3. How do you solve 2 trig equations?

To solve 2 trig equations, you can use algebraic methods such as substitution or elimination. You can also use trigonometric identities and the unit circle to simplify the equations and find the solutions.

4. What are some common strategies for solving 2 trig equations?

Some common strategies for solving 2 trig equations include using the Pythagorean identities, factoring, and using the inverse trigonometric functions to find reference angles. It is also important to check for extraneous solutions.

5. What are the applications of 2 trig equations?

2 trig equations have various applications in fields such as engineering, physics, and astronomy. They can be used to calculate distances, angles, and heights in real-world situations. They are also used in creating graphs and models for different phenomena.

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