Solving Simple Trig Identities Homework Problem

In summary, the conversation discusses simplifying the expression f(t) = sin(\betat)*cos(\betat) using identities. After some initial attempts, the conversation leads to using the identity 2sinxcosx = sin2x to simplify the expression to f(t) = (1/2)sin(2\betat).
  • #1
Sneaky07
6
0

Homework Statement



Simplify this expression:
f(t) = sin([tex]\beta[/tex]t)*cos([tex]\beta[/tex]t)

Homework Equations



Identities

The Attempt at a Solution



I started out by doing sin([tex]\beta[/tex]t)*sin([tex]\beta[/tex]t+[tex]\pi[/tex]/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original formula which it should. Anyone have an idea? Just the start would be MUCH appreciated.
 
Last edited:
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  • #2
You have f(x) but no x anywhere on the other side. What is the variable and what is constant?
 
  • #3
Sorry about that. It should be f(t).
 
  • #4
The first thing that came to mind was 2sinxcosx = sin2x
 
  • #5
Ahh! I think that is what I needed. If 2sin(x)cos(x)=sin(2x) then I can multiply both sides by 2 which gives 2f(t)=2sin([tex]\beta[/tex]t)cos([tex]\beta[/tex]t). After, just carry the 2 over so you get f(t)=(1/2)sin(2[tex]\beta[/tex]t). Thanks man!
 

FAQ: Solving Simple Trig Identities Homework Problem

What are trig identities?

Trig identities are mathematical equations that involve trigonometric functions (such as sine, cosine, and tangent) and their reciprocals. They are used to simplify and solve trigonometric expressions.

How do I solve a simple trig identity problem?

To solve a simple trig identity problem, you need to use algebraic manipulation and the properties of trigonometric functions to rewrite the expression in a simpler form. This may involve using Pythagorean identities, double angle identities, or other trigonometric identities.

What is the purpose of solving trig identities?

The purpose of solving trig identities is to simplify and manipulate trigonometric expressions, which can make them easier to work with and help solve more complex problems. Trig identities are also important in many fields such as engineering, physics, and mathematics.

What are some common mistakes to avoid when solving trig identities?

Some common mistakes to avoid when solving trig identities include not using the correct identities, forgetting to use parentheses when substituting values, and making errors in algebraic simplification. It is also important to be familiar with the properties and rules of trigonometric functions.

How can I practice and improve my skills in solving trig identities?

The best way to practice and improve your skills in solving trig identities is to do lots of practice problems and to review the properties and identities regularly. You can also seek help from a tutor or online resources, and work with a study group to discuss and solve problems together.

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